The British Gliding Association Manual - Sample

7/25/2019 The British Gliding Association Manual - Sample

1/32

T

he British Glidin

g

ssoc

iation anual


2/32

o t

W

hilst

e

very ef f

or t

has

be

en m

ad e

to

ens

ure t

hat th

e

co

ntent

o f th

is bo o

k

is a

s

te

ch ni c

ally ac

curate

an

d

as

so

und

a

s po ssi

ble,

n

eithe

r th e

edito

rs no

r th e

publi

shers

can acc

ep trespo

nsibi

lity

fo r

an y

in

ju ry

or

los

s

su

staine

d

as a re

sult

o t

heu

se o this

mat

erial.

F

irst

p

ubli s

he d

in

200

2 by

A

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lis he r

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he

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I

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All

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erved

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art

o th i

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ublica

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an ymeans

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al ,inclu

ding

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tocop

ying,

re

co rd i

ng , tapin

g or

info

rm at

ion

stor a

ge

a

nd

r

etriev

al

sy

stem

s w

ithou

tth e

p

rior

perm

issio

n

in

w

ri tin g

of

the

pub

lis he r

s.

The B r

itish

G li

ding A

ssoci

at ion

ha s

as

se rte

d its ri gh

t

u

nder

th e

C

opyri

ght,

De

sign and

Pate

nts

Act, 1

988,

to be

id enti

fi ed

as the au

thor

o

th is

wo rk

.

A

C I

P cata

lo gu e

reco

rd for

this bo

ok

is availa

ble f

ro m th e

Briti

sh Libra

ry .

A ck

nowl

ed ge m

ent s

C ove

r

ph

otog

raph

court

esy o

Neil

Law

son

Lin

e

d

iagram

s by

Ste

ve L on

gland

T

ypese

t in

M in

io n

Displ

ay 10

/12 p t

Pri n

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nd

ou

nd in

G re

at B

ritain

by

Bidd

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Ltd, G u

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n


3/32

The

British Glidi

ng

ssociati

on

M a

nua

C

BL CK LONDON


4/32

Contents____

________________

Acknowledgements

vi

Introduction vii

Chapter Definiti

ons 1

Chapter 2 Faltering

steps

27

Chapte

r

3

Lift drag

and the

boundary

layer

59

Chapter 4

Fo

rces

in

flight 95

C

hapter

5

The

placard

structure

and

flight limitations

115

Chapter 6 Stability

and

control

163

Chapter 7 Stalling

and

spinning

197

Chapter 8 Gliding and performance

221

Chapter 9 Variometers

239

Chapter

10

Meteorology

257

A

ppendices

293

Bibli

ography

3 3

British

Gliding Association

contact details

3 4

Index

3 5


5/32

cknowl

edgeme

nts

Graham

McAndrew,

fo r

large

parts

of

the text

and

a

number

of

drawings.

John Gib

son, whose tireless efforts and patie

nt

advice

have help

ed clear up a number of fundamental

points,

and

wh

papers and drawings

have

provided

the

basis for much of the new material.

Pete

r

Bisgood

for

his

advice and unflagging good

humour

w h

en

faced

with lots of rather stupid questions.

Tom B radbury, whose profound understandi

ng

of

the w eather has

been

invaluable in

the meteorology section.

sus

that, like m e he thinks that trying to describe

the w eather

in

30 pages or so is a mark

of

lunacy.

Andy Walford for his knowledge, expertise

and unselfish

help.

Alan

Dibd

in ,

whose clarity

continues to

amaze m e.

David

Owen,

John

Dadson,

Afand

i Darlington, Dave Bullock

and others who

have

offered

pertinent criticism

helpful

suggestion s

.

M y thanks

also to the various

beta-readers w ho have ge n

erously ploughed

th

rough various drafts

of draft chapte

check their general

comprehensibility. They do

ot

seem to have been

irretrievably brain damaged.

Also to

the

E G A for all

owing the

use

of

some drawings and text

largely

from Sailplane

6

Gliding.

Fina

lly

to

anyone who

has

contributed either witting

ly or unwittingly

to this marathon production, an

d who

has

been thanked

by name, my

apologies

and

thanks.


6/32

Int

ro

du

ct

ion

W hat

do you

need to

know

Originall

y

aimed

at giving

gliding in structors

a general feel

for

how

gliders

work,

t

his book is not

a Technica

l

M anual

in the us

ual s

en se,

an

d veers of f into

areas

not

directly

relevant

to

the

bas i

c theory. Some

readers

may

find this irri

tati

ng,

but

there is no statut

ory requirement

for

the

entire

bo o

k

to be

read. The index a

t

the

back of

the bo

ok refers

re

ad ers

to

the

chapter su

mmaries, w

here

co

ncise de

fi

n

itions can

be found, and the

summaries po

int to

the

rele

van t

page in

the chap

ter where the

re

are

fuller

explanations

.

A few summary

items

may

no t

refer to anything

explicit in

the chapter

text,

and

are

thereto

tie

up

a

few

loose ends.

It is de batable which

pa rts o

f the

theory

a

glider pilot

n

eeds to

know, an d

in how much detail

.

Idea

lly

e

veryone

wou

ld beinterested

in the theory, but

it is of ten see

n as:

(a )

difficult

.

It woul

d

be

a lie to say that

it

was

al

ways

easy, but it

is of t

en

very

straightforward if

you

keep your

head. Par

adoxically,

a

nd ra ther an

noy-

ingly if one

is

clearly failing to

get

th

e point, the

extreme

sim

plicity o

f

s

ome of the theory ca n

make it

difficult to grasp

(b)

in tellectual. In

themost insulting

se nse,

intellectual

is tabloid-sp

eak for

useless. Arguing

that

this

is untrue woul

d be re

garded by such

publicat

ions

as

intellec

tual

(c) requiring

a brain the size

of a planet. Not really.

(d )

A

couple of attentive

neurons is us u

ally s

ient, plus

a

bi t

of im aginatio

n

causin

g eruptions of spots

and pimples.

If

you are interested

in

h

ow

useful Theory can be

subject isdiscussed

in chapter

two as

part

of the Re

q

ments for

Flight.

Rather than

p

rovide

a vast list of item

s

which

ca

skipped and

t

hose w

hich can't, th e contents pa

ge of

chapter

has bee

n

coded

. Items wh

ich glider p

instru

ctors in

pa

rticular,

ought to know about

ar e

ma

with a . Lessimportant

items

about

which you

ne

know some

thing, bu

t where detailed knowledge

required, are marked with

a ^r.

Anything

unma

rked

be l

argely for interest.

The

M e

teorology ch

apter ha

been coded

bec

ause

if

you want to kn

ow

a

bou

weather

you

need

to

kno

w all of it,

and

quite

a lot m

It has been suggest

ed by friends

in

e

ngineering

science

th

at I state that

I

am

neit

her an

e

ng ineer

scien

tist. Prob

ably

as

a re sult of being

a

gr ap

hics

trator, there

will

be errors

in

this

bo ok,

and

they

w

my

fault,

either

th ro

ugh misunderstand i

ng somethin

been told,

or

sim

ply

not

believing

it.

Whate

ver e

ls

book might have

set

ou

t to d

o,

it

certainly do esn t cla

be the

last word on

any theory.

Readers

c

an re

st assured

that

w h

atever the

cu

theory happens

to be, reality

will continue to work a

or a

s

badl

y as before.


7/32

ch pter

Definitions


8/32

C

ha

pt

er

c

on

ten

ts

^ -

sh o u

ld k

n o w

-u

se

Scar

y s

cien

ce

......

.......

......

...

P

hysics

in

t

he F ie ld

t Dim

ensio

ns

.

......

......

.......

..

G iving

dire

ctions

-

startin g

fro

m whe

re

Co o

rdinate

s (y o u

are h e r e )

A lg

eb ra and be

ing

lo s t

Ti me s arro

w

F

orces

, vecto

rs,

lo

ads

..

.......

......

......

.

E

quil

ibrium

..

......

......

......

W

eight

, grav

ity an

d

mas

s W

, G and

m

) ..

......

.......

......

.

I

nerti

a

....

......

......

......

Mom

entu

m

.....

.......

......

....

Chucking one sweight

about

......................

A

cce

lerat

ion not

due

to grav

ity

.....

.......

......

....

Ce

ntre of

g

ravi

ty

(CG

),

ce

ntre

of

mas

s .

......

......

.......

..

F

allin g o

ver

C G

w

hen th

ere s no

G

M

om

ents

and l

evers

...

.......

......

......

V

ecto

rs

and

the

resol

ution

of

force

s

........

.......

.......

...

Odd

couple

s

t

E

nerg

y an

d

energ

yco

nver

sion

......................

Potenti

al an d

ki

netic

energie

s

t

Pack

ets an

d

par

cels

..

......

.......

......

.

t Fram

es o

f

refer

ence

.

......

......

.......

..

Cha

pter

sum

mary

.

.......

......

......

..


9/32

fini

tions

Skip

this

c

hapter i

you

are

famili

a r with ba

sic Physics

c

ary

sc

ience

Whatever your

views about

w

hat sc ient

ists do,

what they

th ink they re doing,

and how and

w hy

they

go

abou

t

doing it ,

there is no question

that sc

ience

is

the

most power

fu l tool

ever

to

come in to the hands of th

e hu

m an

ra

ce.

No

oth

er w ayof lookin

g at the

physical

worl

d

has anything e

ven remotely approaching

science s

practical

horsepow

er,

and in

terms

of

o

ur

understa

nding it has been both

hugely su c

cessful

and, i

t has to be

said, occasionally

woundingly

destruc

tive.

Either

w ay , it

ha

s changed fo r

ever how

w e

look

at

and see

th e

w

orld and ours

elves,

and, like it or

not, will continue

to do so in w ays we cannot

even guess.

Scientists

are not always

science s best amba

ssadors, and non -scientists don t

always

take

kindly t

o being told they don t

really know

anything. W orse, when m athem

atics is

wheeled out to provide eleg

ant and logical proof of so

mething t hardly matters

w hat

many of us ex perience

an overwhelming

desire to

become

completely

unconscious

.

In

fact, a

general

understandin g

of how

gliders workdoesn t need anyth

in gmore

elaborate

than

the

three apples plus t

w o

pears

variety of arithmetic. W e

do, however, need to

un

derstand ba

sic physics, as without it

w e have li t

tle

chance of

real

is ing

how

a

gli

der

manages

its tr icks.

This first c

hapter looks at

some of

th e

basics , with many

of the examples

being

taken

from gliding.

In fact, yo ucan check

out most of the physic

s

f

or

yo u

rs elf by doing

nothing

more strenuous,

mentally or physic

ally, than

goin

g to an

airfield

a

nd

either

taking

a

fligh

t,

or just

pushing something

around at the launch point.

hysic

s

n

the field

The l

ist below

contai

ns a se lection of

airfield

ac

tivities

and some

o

f the relevant

physical

laws, for th

e

momen

t

stat

ed

without

any

explanation:

helpers som

ehow manage to run

a glider o

ver

yo

ur foot.

The

pain you feel i

s a

result

of

t

he glider s weight (

weight equals

mass

times

gravi ty

you

are

momenta rily distracted

by

something

else

on the

ai rfield.

Helpers

run

the glider

into you

r back.

The

pain you feel is

related to the glider s

momentum

(mome

ntum equals

mass

times

ve locity

yo u

land

on a runway. Helpers

come to push the

glider. Even

though

th e surface

is smooth

and flat, the effort yo

u have to

m

ake

to get the glider

mo

ving,


10/32

The

British

Gliding

Association

Manual

particularly if this needs to be done

in a hurry, is far

more than

what s

nee

to keep it moving once

it s

rolling. The difference is due to inertia (Newt

First

Law ofMotion)

the

effort you expend pushing

the

glider also demonstrates energy conver

(breakfast cereal

into

bodily movement)

and

illustrates something

about

vec

(force(s) applied

in

a

specific direction)

to manhandle

a

Kl3 with

two

people

already

on

board

up the launch

queue,

first

have

to push

down

on

the

tail to lift the nose-skid off the ground. f

move closer to the wing

you

have

to push

down

much harder to get the s

result

moments

and levers)

you

have

a

cable

break

on the launch.

A s

you push over

you

experienc

reduction in your

weight acceleration,

Newton s

First

and Second Law

Motion).

W e

spend every

minute of

every

day demonstrating

these

and other laws to

oursel

even

if we aren t

aware of

doing so. W hat is

important

about all

the examples given

ab

is

that

the

physical

laws

they

illustrate

describe things which,

apart

from the

specific

inju

mentioned, happen with a high degree of regularity

and

predictability; all of which sugg

that the world has a natural

and

inherent order, as

indeed

appears to be the case.

imensions

W e ll take it as read that the physical world exists. If we

think about why

it works in

way

it

does

rather

than in any other

way,

then most

of what

we take completely

granted

turns

out to be a bit

strange,

to say the

least.

Take the space around

us.

Eac

us

lives

at the centre

of

a

sphere

of perception d otted with

objects

that

are

separated f

each other by well, by what

exactly? Empty

space? Nothing? W hatever it is,

witho

none of us would be anywhere.

It is useful to think of this space as either containing or consisting of three rel

physical

dimensions (figure 1), at

right angles

to each other.

Despite the

world s

hills

and valleys,

we

spend

most

of

our

life

pinned by gravity

to

surface of the two-dimensional plane represented by figure 1 example

(2).

A s with

much of the natural toolbox bequeathe d to us by Nature and evolution, we are not

aw

that our existence is governed

by

the

need

for us to

continually measure

and calcu

where we

are

within the

surrounding space. True, we

don t

leap

about

saying x

+y

or d=r x

a ,

but if we weren t

doing

something similar

we

would not last very long.

information required by the brain for

the

necessary calculations and comparisons

co

from

two

main sources:

(1) force

information

provided by the semi-circular canals in each

ear,

and sensat

from other

parts of

the

body,

particularly

the feet

and legs (tension

in the mus

and

so

on )


11/32

fini

(2 )

visua

l inf

ormat

ion

from

th

e ey e

s

t

ions,

angl

es, dis t

ances

).

(

direc-

A n

app

arentl

y co

heren

t an

d f

luid

reality

is

c

onjur

ed o

ut of this

in

form

ation,

but ittak

esti

m e to

create

it, ho

w eve

r sh o

rt, so ou

r pe

rceiv

ed w o

rld t

rails

a

fra ction

of

a

se con d

behind

the

real

one.The brain

a

lso

h

as

an

ed

itoria

l f

uncti

on,

and is mas

terly

a

t

igno

ring th

ings w

hich

dont

fit

. Fac e

d

with

a

contr

adict

ion, or a g

ap t

hat

'sho

uld n

ot

b

e th

ere', it

wil

l m ak

e

some

thing

up. Ju s

t ho

w much

of our

ex p

erienc

e is sn

ea kily

extem

por i

se d

in this

wa

y is

o

bviou

sly

diffic

ult to

sa y .

Ex

actly

how th

e brain

dec i

de s

w he t

her a se n

so ry

i

nput is

w

orth inc

lu din g

in

its w orld

view

or

no

t

is

ano

ther m

atter.

Pil

ots are

well awa

re w he

n fl

yingi

n

cond

ition

s of g

ood visib

ili ty, t

hat w

hen

they

ba nk

,

th yare

ti lt ing

and not

the w orld. W hen

circlingin

c

lo ud

or ve

ry po

or visib

ili ty,

visu

al inpu

t fa lls be

low

so

m e

criti

cal thr e

sh old

,

and up be

come

s a

lm os

t

e

ntirel

y dep

ende

nt

on th

e sensed

,

or app

arentdi

rec

tion o

f gra

vity.

In a ba

la nc e

d tu

rn th i

s is

straig

ht

dow n

our

spines

, i. e .

in t

he uprig

ht di r

ection

.

In

ea ch e

ar we

hav

e

t

hr ee se

m i-c

ircula

r cana

lswhic

h

lie

at

r

ight

ang l

es

to ea ch

other.

The y

co

ntain

tiny

l

ime

cr

ystals

w

hose

conta

ct w ith

se

nsory

h

airs pro

jectin

g

in t

o

the

ca n

als su

pply

th

e b

rain w ith

in

form a

tion

ab

out

orien

tatio

n and

ac ce

leratio

n. Du

ring

a

constant

and ba lanced

turn

the

crystals

settle

onto

se

nsory

h

ai rs a

ss ocia

ted

w i

th 'upr

ight'. W

itho

ut

i

nstrum

ents

or an y

othe

r

inp

ut to

c onfi

rm

or con

tra

d

ict th is m

essag

e,

the b

rain

takes it to

m

ean,

qu

ite l

iterall

y ,

upr

ight

asi

n not b

an kin

g'.S t

ill

t

urnin

g,

w e su d

denly

po

po

ut of

cloud

, an

d the w or

ld appe

ars

to

have

fallen

ov

er. W e

fe

el

distin

ctly

sickw

hile th

e

brain

r

eadjus

ts itself

.

The re

aso n

for

m

ntion

ing

an y

o

f these

th

ings

is t

hat (

a) there

c

an be se

rious

disc

repanc

ies b

etwee

nh

ow

we

see the w or

ld and

w

hat'sr

eally

happe

ning

(thisbeg

s

a few

que

stions

),

a

nd

(b )

o

ur pers

onal s

ense

of w

here

we

a

re

is, in

the

most

ge

neral sen

se

of th

e

term

,

self-

centre

d,

a

nd it's d

ifficul

t to s

ee ho w

it co

uld

be any

th ing

else.

S om

e of th

e

res

ults o

f

t

hi s can

be c

on fus

ing Y o

u poi

nt a

t th

e sky

and say

'tha

t's up . On

the opp

osite

side

of

the w or ld so m eo ne

e

lse do es

thes

am e

thing.

A rem

ote obse

rver

w ou

ld

see tw o

p

eo ple

point

ingin

co

mplet

ely

oppos

ite dire

ctions

.

W ha

t we

tak

e to

be up

is

a univ

ersal

stan

dard

onl y

in so

far a

s

e

veryb

ody

re

lates it

to t

hemse

lves. 'U

p ' is

dete

rmine

d larg

ely by

o

ur bo dy '

s

orient

ation

, and th

e direct

io n o

f an

y force

s acting

up

on it.

S ince

the

m ajo

r

f

orce

to w hic

h w

e ar e su

bjecte

d ap p

ears

to

be weigh

t, an d

, by

as

sociat

ion,

gra

vity, up

norm

ally m

ea ns he

ad a

t th

e top

and

feet at

the

b

ottom

'.

i

gu re Th

ethree

im

ensi

an

d ass

ociated

plane

s


12/32

The

British Gl

iding ssoc

iation Manual

G

iv ing

directio n

s

s

ta rting fr

om w h

ere?

If there

w a

s

only one

person on the plan

et, the self-c

entred

view w ould be

ne

ither

n

or

there.

One could

believee xa

ctly whatone li

ked. Su

ddenly, someon

e else appears

t

hey are

askingfor direc

tions to

some place. Once

ov er the

shock, w hat

does one

act

say?

Not much if

w e d

on t

know

where

w e are in re lation to this

other place. f

w

know

,

then w

e

have,

in

effect, to

create a map,w

hich implies m

easurement

.

W ay

back,

th e s tandard might

have

been th e length

of

the rulers

fo ot.

Systems

b

on one

perso

n s physical quirk

s,

ho

w ev er

regal, are hardly

id

eal.

The

ruler

will

die

an

foot

go

w i

th him,

causing economi

c

and

soc

ial d

is tress. Mayb

e

the foot

could be

cu

and pickled,

ut fa r

b

etter

to

persuade

him to sanc

tion an accurate

reprodu

ction

t

copie

d by

th e

th ousa

nd. That way ev e

ryone

has access to the fo

ot, whe

rever the orig

a

nd it

be c

omes

an independ

ent, neutral,

and

pu

blic

standard of m

easurem ent.

In

w h

atever way a m

easuring syst

em/s tandard

is se t up,

it mu

st have:

a consistent

and agree

d se t

of

uni

ts (e.g.

walk 35 pa

ces )

an imag

inary and u

sually regu

lar grid centred

on a

fixed origin (e.g

. start

h

ere)

a

location

defined

on

the

grid

by

at

least

tw o,

possibly

three unique

piec

information

(e.g.

go east unti

l

yo u

meet the

river

, then

w

alk one m

ile

nor

Figure 2

M ap

s

two

dimen

sion l c

oordin tes

Origi

n of the

map grid

graph

1

1

e

ft ight

10

Coor

dinates

y

ou

a

re h

ere)

To pin

point

the po

sition

of anythin

g

on a

or a gr

aph

bot

h

tw o-dimen

siona l

grids

m inimum

of

two

coor

dina tes

ar

e needed,

for each

dimension.There s a

le ft

/right

co o

nate,

and a forwa

rds/backward

s coordi

ea

ch

d

efinedin

relation to

the

grid

s o

rigin

ex

ample, if you stand

at position

A in

figu

yo

urcoo

rdinates are fo

rwards eight

le

ft

nin

p

os ition B yo

ur c

oordinates w ou

ld be b

wa

rds

tw

o

right three.

Whil st two

coordina

tes are enough to

d

a

po

sition on

the

surfac

e of a

m

ap, a m

inim

of th r

ee are needed to

de scribe

any po s

above

it (figure 3 ).

T

heres no

point ad

extra

dim

en sions

if

all

they

do is

du pl

inform

ation

y

ou

already

have, so

on

th a t c

alone

the th

ird

dime

nsion

must be at

a

ngles

to

th e

other

two.

Position

s

ca

n also be

defined

us i

ng a

be

and

distan

ce

from

a

know n

point, e.g. five

so u

th west

o

AstonDown.

Our

height

will

describing in

te r

ms of

ano ther angle


13/32

1

finit

says

noth

ing

abou

t

Y

either

X

nor

Y

say anything

aboutZ

e

levation

or asa vertic

al dis

tance

abov

e th e

end

of

th e

li ne

from

the

o

rigin.

A

lgeb

ra

an

d

b

eing

l

ost

D e

scribi

ng

a po

sit ion

i

n term

s of

coord

in ates

is stra

ig htfo

rw ard if

yo

u h

appen

to k

now

w

here

you

are.

I

am th

re e

mile

s

due west

of

th e Lo

ng M y

nd

a t

3

,5 00ft,

you

m ig

ht

s a y

But

wha

t

if

yo

u re

lo

st?

M

os t

of

us a s

socia te

n

um b e

rs w

it h

spe

cif ic

thin

gs: th e r

e a re th

re e a

pples

in the

fr

uit

bow

l

an

d m

inus tw

o

hu

ndred

po

unds

in

th

e

curren

t

a

ccou n

t. Easy s t

uff,

yet

con

front

u

s

with

n um

b ers w

hich a re

n t

s tu ck l

ik eflags

t

o objec ts

,

or

fla s

h

u

s

ari thm

etic

with

a lpha

b

e tical

b its he

c

ur sed

a lg eb

ra

and the

IQ

gauge

falls

to z

ero.

Thi

s

i

s

a

very

odd re

act ion

bec

ause a lo

t

o

f

wha t we

sa y

(a nd d

o) i s

suspi

c iously

a lge

b raic.

For exam

ple , w

e

m ig

ht reca l

l tha t

th e r

e

was

frui

t

in

th e

bowl

,

ut

n

ot h

ow m uc

h

or

ev

en

wha t

so

rt. W e

w ou

ld n t thin k

tw

ice ab

out

sayin

g, I kn

ow

th

ere s

som

e fruit

in

the bo

wl, b

ut th o

ugh

ess

entia ll

y th e

sam e th i

ng , w

e

w ould

n

ot

say

th

ere

a re X f

ru it(s)

in t

he

b

owl,

wh

ere X

is a

nu

m ber. A

mathe

mat ic

ian m

ight d

escrib

e

the s

ituatio

n th u

s , but g

o fu r

th er

a nd

lop off

a nything

even

a

whisker bes ide the

point ,

l

eaving

us w

ith a fruit-

bowl-

conten

ts-pro

b

ab i

lity-fu

nction

such

a

s

X

F R U I

T

or so

m ethin

g

equ

ally c

ryptic.

W he

th er

lo

s t

in

fl ig h

t or no

t,

ou

r

positi

on req

uires

th r

ee coo

rdinate

s to des

cribe it,

e it her

ex

actly

(we

know

the n

um ber

s) , ap

proxim

ately

(we know

s

ome

o

f t

he nu

m b e rs

),

or

abs tr

actly (w

e hav

en t

th e

f

a in te s

t

id

ea

w

hat the nu

m bers

are,

but w

e

kn

ow the

y re

need

ed). If ask

ed, we

cou

ld d

escribe

our

un

certa i

n lo

cation

as a t

c

oordin

a tes X Y Z

, where

X

is

a long

, Y

is up, a

nd Z

is a t ri g

ht

an

gles

to X

a nd

Y

(f

igure

3). W

ithout

the num be

rs ,

this

is

a

b out

as help

ful

as

saying

H

ello,

I m some

where

.

levati

on an

d dis

tanc

Fig

ur e

3 Th ree

dimens

ion

coo

rdinat e

s

Tim e

s arr

ow

T

ime

is

a

lso a d

imens i

on a

n d a c

oordin

ate. A fou

r-dim e

nsiona

l po

sition repo

rt

wou

ld

be

so

me thi

ng lik e:

I

knew whe

re I was

a t

four

o

clock.

Even thou

gh we a

re

awar

e

of

ti

me,

it s pr o

bab ly

tr ue

to say t

ha t no-on

e r

eallyk

now s

qui

te w ha

t

it

is th

a t

clock

s are

ac

tually

m e

asurin

g .


14/32

The

British

GlidingAssociation Manual

V

olume

Length

Depth

Width

Mass

Speed

Forces

vectors

loa

ds

Figure

Quantities

Wher

eas

objects

are

visible,

force an

d

energy are

only

so

in directly. Like m

any biolog

and biodegradabl

e

entit

ies, w e are in the

unusual position

of

being aware of

the exp

diture of energy

(what an effort), and can sense force

(I was hit), without being able

to

either of them. In order

to

applyf

orces ourselves (move

this),

w e

have to burn some o

en ergy

stored

in

our

bodies,

and then

eat to

replenish

the

store.

On that

basis

w e

m

co nclude that only biologic

al org anisms

have

energy and can apply force, but

inanim

objects can have

plenty of

both.

You can prov

e th is by dropp

ing a brick on your

foot

Volume,

length, depth, width, mass

and speed are

scalar

quantit

ies. A vector on

other

hand, is a quantity which has both

magnitude and

direction. Velocity w hic

sp

eed

in

a

s

pecific direction, is

a

vector, as are

gravityand weight (figure 4).

Loads

are

the

in

ternal

response of a

material to an

applied

force, and hav

e

independent existence. For example,

if you hold

a

rod just

to

uching

a

w all (figure 5)

pressure orforce is ap

plied until you pushthe rod again

st

it.

The 'push ' then becom

load whic

h

is

transferred through the rod's ma

terial to thewall. Loads are vectors.

Figure 5

Loads

and

the

transference

of force

Load

tran

sferreddown rod......

....and a

pplied here

k

i

l

3

*;

x S ,

.4

-

-H

4

-

- e f t

^W l-(

8 5

3

f e

3

Equilibrium

Equilibriu

m

is a

condition in w

hich all

th e

forces involved ba

lance out,

but t

hat doe

necessarily lead

to th ings being steady in the

conventional sense of the

term.

A n

ob ject

be

in equilibrium whe

n

it s

motionless, and

when it is

ripping alo ng at

se

veral

hund

miles

an

hour

and tumblin

g

crazi

ly

end

over en d

. Equ ilibrium

can be

very dece

ptive

hide

extreme

forces,

as seen in the fol lowing example

. Out of reach in the

flames

of

garden bonfire is

an empty

aeroso

l can. The contents are

expandin

g

in the heat

and

internal pressure s rising,

y

et nothing

appear

s to

be

happening.

Suddenly the

c

an explo

Shrap

nel

and

fragments

of

bonfire fly

all

over

the place. S o much for equilibrium

Weight

gravity

and

mass

W,

G

and m__

_________

_________

It

i

s doubtful w

hether,

in our everyday

lives, any

o

f us make

distinction between mass

weight,

an

d

there's

no

re a

son

w hy w e

should. Had

the distinction been

cr u

cial

to


15/32

ef

in

survival, then na t

ural selecti

on would hav

e shaken out se

nse organs

capable

of di

sting

uis hing

between

the two,

b

ut

it di

dn't. Nor did

it equip

us

s

pecifically fo

r flight,which is

an

ar

ea w

here

th e

di stinction be

tw een m

ass

an

d weig

ht is m ore obv

io us and, i

n so m

e

re spect

s,

far

m ore critical.

Pilots

are

fa m iliar wi

th how man

oeuvring in flight

can a

lter

their

weight to zero, or

to so

heavy that

they

cann

ot move

. That thes

e chang

es occur at

al

l

is significan

t eno ugh

, but

ev

en if we

m

om entarily weig

h nothing we

don t as a

re sult win

k

ou

t o

ex istence.

Pinchyourself at the appropriate

weightles s

moment

during

a

vigoro us

pus

h-overafter

a

ca

bl ebre

ak

and

,

yes

,

you are still

there. This im

plies

that

even if

weight

is

an in

consistent

and,

in

deed, an unr

eliable qua

ntity, th

ere

i

s someth in g

else

wh

ic h is not.

That

something else'

is

mass,

and

coul

d

be

d

efined as

th

e stuff left

over w

hen you've

taken

weight away'. Mass

creates the fo r

ce

w

e kno

w

a

s gravit

y,

and

gravity

creates weight.

An

ything with m

ass will attract

an yth i

ng

e

lse wh

ich has

ma

ss, so we

ightde

pends to a

cert

ain extent

on

who is

having the greates

t

effe

ct. We att

ract the Ea

rth to wards us,

b

ut

with

little re

sult

gi v

en th e scale of

its

effe

ct on us.

It is co n

venient, theref

ore, if not st r

ictly

accurate, to

th

ink

o

th

eEarth as

bein

g

t

he

on

ly source

o gravita

tion at its surface.

Since the

Earth's m ass is effectively

acting upo

n itself, t

he planet's nat

u ral shape is a

sphere. A

fa ll

ing object will

accelerate towards

the Eart

h's ce n

tre

at a con

stant rate of

32

fe e

t

per

second,

every se co

nd (32ft/sec or

9.8m

),

but if already on

solid ground,

it can't

get

to wher

e

it is

being dra

wn, so one can l

ook

upon

weigh

t

as

th e frustr

ated acceleratio

n

om

ass. That's not

to sugges t

that w

ei ght is an

illusion ry

liftinga grand

pia no o

n

y

our

own ust that

i

t isn't quite what

it seems.

Tw o

further poi

nts n

eed to bem a

de

abou

tgrav

ity and mass:

(1 )

two objects of d

is similar

mass but si m

ilar volume, dropp

ed tog

ether,

will

fall in

ta

ndem .

The

effectso

f air

resistance

are

considerab

le, so this is

ha

rd to demon

s

trate

Assu

m ing

no

air resi

stance,

a

large ball of

ex p

anded

p

olystyrene dropp

ed

fro m

a

high tower w

ill

ac c

elerate d

ownwards

at thesame ra

te

as

a le

ad

ball

of

i

dentical

v

olum e, and

they

will re a

ch th eground

simultaneo

usly, i.e. at the

same

ve lo c

ity.

Here'sa

practical tip

: air resistan

ce

or

not, if

you

ar e

going to be hi

t by

either, m ake sureit

is n't

the lead

ba ll

(see

inertia

and

momentum

below)

(2)

when we stand

on any s

olid surface it

pushes passively

up

wards

against us with a fo

rc eexactly

equal and

opposite

to our

weight

(figure 6).

f the ground's

re ac

tion

we

re an yth

ing else

w

e

would

either s

ink

out

of sight or

be hur l

ed into th

e

air.

Th

e

normal

pa s

sive re a

ction has conseq

uen ces f

or

flight

in

that,

if

air craft ar

e

to

fl

y

at

all,

an

upward fo rce must a

ct upon them

which

is at least

equal

to

that

pro

vided by t

he

groun

d

when they

are

sat in th e

hangar.

suffer

ed in the irst

two

examples of

airfield acti

v

on

pages

3 4 he h

elpe

runnin

g the glider over y

fo

ot

the

n

into your back

ha

ve an

identic

al

cause.

even

though weight

was

responsible

wh

en

the glid

ran over

yo

ur foot

it

h

ad

nothi

ng

to

do

with yo

ur

p

when the

glider ran

into y

bac

k

Fi gure 6 Ground gravity a

weight

Since th e

strength of

Ea rth's gr

avity is br

oadly constant

at the Earth's

surface

and

within the

waf er

thin

layer

of

the atm osphere where

we

conduct

most of

our

activities, it is

treated as a co

nstant

and, fo r

conven

ie nce, 3

2ft/sec

i

s

regarded

as

1G.

C

om forting

to kno w

,

bec

ause,

ev eryth

ing

else

bei n

g

e

qual, the g

lider whi

ch

injur

ed us earlier will

always

weigh th e

same

a

mount no

m tter how

often

it is run

over

ou

r f

oot.

Gravity accelera

tes

the body downwa

rd

Ground pushes upwa

rd

Result

= normal we

ight


16/32

he

B

ritish Gliding ssociation Manual

Inertia

Weight M

ass

g

or

W

mg. If

g

then W

Weight

Figure? Spring balance and

glider at rest

The same cannot alw ays be said of inertia which s the irritating

thing

that

makes

object,

particularly a large

one

like a glider, difficult to get

moving and

then

equally h

to stop. Even though mass and

w e

ight are related (see box), an ob

ject's inertia s dep

dent

solely

upon its

mass;

the greater the mass of an object,

the

greater

the effort requ

to

start

it

moving

or bring

it

to

a

halt.

M

easuring

inertia is not straightforward.

Experimenters are constantly

faced

by Natu

prodigal habits, a

nd

detail w hich they

would like

to

study

is

surrounded by equally insis

detail

jostling for

attention, and simply

ge

tting

in

the way. The cleverest part

of

exper

im

aimed at m easuring

some

thing specific often lie in avoiding

measuring

anything

else

example,

try

to measure inertia

by moving

a

glider on

soft ground

and the

wheel wil

a

deep

hole

and

want

to

stay

in it. Most

of

our effort goes

into trying to

shove

the gl

up an effectively en dless hill, and has nothing to

do with

inertia.

There are easier w ays of observing

inertia

at work than

pushing

a

glider all

over

place.

Take

a spring

balance and hang

a large

object from the hook (figure 7). The re

s

a

minimalist

m

odel of a glider at rest on the

ground.

Normal ly w e w ouldn't attemp

lift a glider

straight

up

into

the

air,

ut that's

what

a

wing

has

to do,

so

the follow

experim

ents will

tell us

something about th e mechanics of flight.

B y lifting and lowering the

balance and

the

suspended

o

bject

several

times

in

the w

indicated, w e

can

come to the

fo

llowing conclusions:

when lifted very slowly

and

steadily the

scale reading re

mains

constant

w he

n

the balance s lifte

d abruptly

the

scale indicates

briefl

y that the suspen

object becam e heavier

he more

so the

quicker

w e

try to

ra

ise it

if

w e

lower the balance very suddenly and quickly

the

scale

reading

r

educes

may briefly register zero

the same moment

ary

loss of

weight occurs if w e

suddenly

stop moving

balance

upwards.

The

m ajority

of these

examples

demonstrate inertia,

and

weight

s affected by acceleration. It

could

be

argued

that w

e

w a

s responsible for some of the effects, but to prove

otherw

we'd have to get rid

of

it. Im p

ossible as

that

might sound,

it

be done.

If weight

s a direct

result of gravity acting on

mass,

gravity

acts vertically

downwards,

then that i

s the directio

which

weight

acts.

All

w e have

to

do

s support the

weight in,

a small cart. The

set-up

s

now as illustrated

in figure 8 .

analogous

to m o

ving

a glider

around on the ground.

Again,

unwanted

effects like

friction can make nonsense

of

the

results,

but

w

allowance has been made for them, w e

note

that a sudde n horizontal

pull

on

the sp

balance produces a marked positive re

ading

on

the

scale.

The swifter

a

nd harder

pul

l, the larger the ini

tial

reading. Scales normal ly measur

e

w e

ight, but

because

the

and the ground have ta ken care of that, w hat w e are measuring s

the

object's

mass

10


17/32

efin

inertia.

Interestingly, the scale would indicate

the object s

weight

if w e a

ccelerated the trolley sideways at

32ft/sec

M

omentum_____

_____

om

entum is the

energy possessed by

a moving object. The

sp

eed

an

d

direction

velocity ) of

an object add energy to the

object s mass.

A

rifle

bullet may

only weigh a few oun

ces,

butfired at poin

t

blank range into a plank

it

will

pass straight through at upwards

of 600mph. If

the

gun su bsequently misfires

and the bullet falls

out

of

the

barrel and bo

unces

off the

plank onto the ground, it

will

be clear that (a)

something has gone seriously w

rong,

and

(b) no

damage has b

een

done. The

only relevant difference

between

the

shots w as the

speed

of

the bullet which, in one case, ad

ded lethal

amounts

of

extra

energy

to

the

bullet s small m ass,

an d

turned

the

other

into

feeble

slapstick.

In terms o the

clumsy helpers

m en

tioned earlier,

the

very practical

result

of

the

abo

ve

is

that

if they

ru n

the

glider into your back very s lowly it wont hurt

nearly

as

much

as

it

will

if they do it quickly.

able to

p

L Measuring inertia

Chucking one s

weig

ht

abo

ut____

Map

coordinates help us locate

where

things are, but

the basic

principles extend

to

objects moving through

3D

space. The flight of a ball

can be treated as two-dimens

ional

because only

two

coordinates

are

needed

to describe

it : a

horizontal

and a vertical com ponent of veloc

ity at right

an

gles

to each other (figure 9 ).

Any ballistic object s clearly influenced

by gravity because if

you

thro

w a ball straight up it

eventually comes straight dow n

again. What is not

s

o obvious is that

this

up

and down

motion,

the

vertic

al

component,

is

unaffected

by any

horizo

ntal component you

give

the ball

when you

throw

it.

The ball s vertic

a l

velocity

in

free fligh

t is gravity driven

an d

will

change at a constant rate.

Ignoring the co

nsiderable

effects o

air resistance,

the

horizon

tal

velocity is dependent

on how hard and

at what angle the ball is thrown

.

Once

in free

fl

ight nothing accelerates or decelerates this component

it

remains constant. The

result s that

re

gardless of whether the

ground is flat

or

not, the

flight time of any ballistic

object s

depe

ndent

solely on

the vertical component of velocity,

i.e. on

gr

avity.

Figure

light

path

components

of

a ball


18/32

T

he

B

ritishGliding

ssocia

tion

Manu

al

F

igure 10

P

arabolic

free

fall

c

urves

Figure A

ngled thro

ws

and

ve

locity/ene

rgy in put

A B

The flight

time

of all

th

ese

throws

is the

same

E

F G

but

n

ot

thes

e

B allistic

objects trace

out

parabolic

cu rves

and

figure

1

shows

tw o

sets

of

th ese.

v

ertical

lines, A and E

re pre

sent a ball

throw n

vertic a

lly upward

s and coming

st

ra

do w n

aga

in .

Ther

e

are

diff

erences bet

w een the

tw

o sets, ut they

have

nothing

t

o

do

w

the

ang le

of any

of

the

throws, only

with the

initial

force.

In

set one, f

or exa m

regardle

ss of th e ang

le, the

ball is alwa

ys th ro

wn h ard

enough to

reac h t

he

s

ame

hei

and

th e

more angled th e

throw

the more

effort

has to

be

m

ade

(figure

1

1). In set

each

thro

w

has

th e

s

ame ini

tial

im p

etus put

in

to

it. As

t

he

angle

of

th

e th row be

co

shal

lo wer, m ore

of

th e

impetus

goes

into

the

horizonta

l ompon

en t

and le ss into

vertica

l one, so e

ach

ti

me the

ba ll

goe

s

le ss hi

gh a nd

hits th e groun

soone

r.

B al l

istic obj

ects in fl

ight

tr

ace out

a fr ee

fall parab

ola, and b

ecause the

ver

tical

ve

lo

co

mponent

is in fluen

ced

solely by gravi

ty (f o

rgetting ai

r re sistanc

e again)

, the

y

weightless .

This probably

doesn t sound

quite right,

so

le ts

take

a

really

surreal

ex am

W

e ve just

fa l

le n

o

ut of a

glider a t a lt

itude and

happen to

h

ave with

us a

pair

o

f

bathr

o

sc ales.

A s we ac

celerate d

ow nward

s at 1G

we are w

eightles s

, or a t

least,

th

a t s th e t

he

we

will no w

check out. W e

try

to sit on the

sc ales.

W hat

do

they

read? A

l

ot, a li

tt le

nothin

g? Con

trary to

e

very thing

we m ig

ht ex p

ect, th e r

eading

will depend enti

re ly

Dis

tance


19/32

De

fin

w

hat

w e do wit

h

the

scales.

For example, if

w e

just sli de them

underneath

us,

they will

read

zero.

If w e pul

l them up against our

backs ides

and

mak e a very determined

effort

to

be sat down

all they willmeasure

is how

hard

w e are trying

ccelerations not

due to

rvity

On

those rare occas io

ns

wh

en

w e think

about acceleratio

n,

w e ten

d to associate it wi

th

pressing do w

n

on a

car accelera t

or

and being pushed

back into

our

seats (figure

12) .

Similar se nsations

occur at

the

start of a winch launch.

Despite what w e feel, we are not

being th r

ust back by

someu

nseen

force

from ahead, but being pushed f

rom behind

and

proving ra ther reluctant to go

fo

rwards

(inertia).

Fi

gure

2

Normal

view

of

acceleration

Foot down

Cars and

w inch launches provide

e

xamples of ' fore

and aft ac celer

ation, reinforcing

th

e notion that

acceleration is

just a

proces

s

of

' speedin

g

u

p'. In

fact,

acceleration can occur

in any dir

ection

and is

funda-

menta l ,

not

only

to changes

of speed brought

about by

putting yo

ur

foot

down,

but

to changes of

direction

where, confusingly, we

can

accelerate

without

al

tering

our

speed

in the slightest.

For instance,

w e are

driving home a t SO

mph from the airfield, an d

reach

a corner

we have rounded unev

entfully ma ny t imes before. Wh e n

w e turn

the

w h

eel now, though,

the

car

ploughs

straight

on

through the

hedge and into a field. The thought least likely

to have passed

through

our

heads s

that on

every

corner,

anyw

he re,

the

car has

lw ys

w anted

to

go

straight on. There is no thing odd about this.

Ploughin g straight on is

the

option in v

olving the least effort,

and ' least poss ible effort '

s

a

majest ically

lethargic principle

that dom inates

the

m aterial world.

We

ma y

sw

ee p ro

und the corner at a co nstant SOmp

h,

but

our

direction

keeps

changing,

so

a

forc e

(an accelerat

ion) must act towards

the centre

of the c

ircle whose c i rcum

ference

w e are

attempting to

fo ll o

w (figure

13) .

Figure

3

cceleration rou

corne

r

onstant


20/32

The

British Gliding ssociation Manual

Figure

14

Stone on a

string

Figure

15 Direction

o gravity

(G )

Figure 1

6 C G

o

two

dimensional shapes

Normally,

when the steering

wheel

is

turned,

friction

between the road surface and

tyres provides the into turn

force, ut this

time there

was ice on the

road,

so

turning

wheel

had no effect. Unable to alter

our

velocity

in any way

what

soever, we bowed

to

principle

of least effort and quit

the

road.

There s

no need to

wreck

a

car

to

understand

what happened.

W

a

stone

a

round

on

the end of

a

string

(figure

14). As you whirl the

st

faster the force

in

the string increases

.

If

the

stone normally weighe

quarter

of

pound

and the

force

in

the

string

was three

pounds,

t

that

would be

the

stone s current effective

weigh.

Three pounds

twel

ve-fold increase, so

the stone was being subjected to

acceler

ation of

12G (3/0.25). The equivalent

of ice

on

the

road

her

to rem

ove

the

inward accelerating force by letting go o f the str

i

Viewed from above, the stone instantly flies off in a straight line

entre

of gravity CG),

centre

of

mass_________

The centre

of

gravity

of

a body is its centre of mass.

Because

the

Ea

is more

or

less

a

sphere,

its

C G is

in

the centre. It can be located

noting in

which

direction

gravity

appears to be acting at various

poi

on

the

surface,

and then extending

these

lines o ction

downwards

their meeting point.

Gravity acts

at right angles

to

the

surf

ace and

we a

re able

to stand

anywhere up o

n

it and be in no danger

of eit

falling

or

sliding off

into

space (figure

15).

Finding the

CG

of a

two dimensional

shap

e cut from

card,

those

in

figure

16 can be

done by

trial

and

error.

Pin shape

A

t

vertical surface

,

making

sure it

ca

n

rotate freely. With

the

pin

pla

in

an

arm, or

along

an

edge, the

sh ap

e will always

try

to hang

sh

own

in

figure

17

This

is because in

the starting

p

osition, ther

always more of

its

weight/area to one

side

of

the

vert

ical line throu

the

pivot than

to

the

other. (The du

mbbells

repr

esent the appro


21/32

fin

mate distribution of weight

to each

side of the pivot

line.

The

arrows

s how the

direction in which

the

shape

will swing w hen released.)

After some

experimentation you ll find

a

piv

ot

poin

t

where

the shape

doesn t swing

w ha

tever the

position

in w

hich it begins

or,

if y

ou sp in

it,

however

fast,

ea ch

and

every

posit ion

in w hich it stops

will

be

a

balanced

one.

Thi

s indicates

that the pin is at the

shape s

CG, as

in figure 18 .

In point

of fact, what has

just

been

describ

ed is

a

monumentally long-winde

d way of locating the

shape s CG. The easiest method

is to pin it

up

by

an

arm, as shown

in

f

igure 19 ,

and

with

a pencil

dra

w

a

vertical line dow

n

fro

m the pivot pin. Usi

ng a different

pivot

point,

prefer

ably as

far aw a

y

from the first

line

as

possible,

draw another lin

e in

th

e sameway . These two

lines

will cross

at th e

CG.

How

yo u would

pin

up

a

shape with an external

C G (figure

1

6

example C),

is

an yb

ody s

guess.)

ivot point

at C G

Figur

e

18

Pivot

a

t

Out ofbalance

n balance

Figure 17

Pivot

p

oint locations

Figure 19 CG t

he si

mple

way

The C G o

f a

two

dimensional

shape

is th e

ge

om etric

centre of

its

surface

area, but the same principle

us e

d to

find

its

CG can

be

ap p

lied to certain ty

pes of 3D o

bject.

Gliders ar

en t spherical, theycontain l

ots of emptyspace,

have no appreciable gr

avitational

effect on anything, and

their mass tends to be

concentrated in partic

ular places.

Even so, working out

a CG position is fairly

straight- ^

forw ard b

ecause, like m o

st

aircraft,

gliders have avertical

^

p la ne

o

symmetry, i.e. left

mirrors right (figu

re

20).

Pro viding

the glider is weig

hed

wing

s level, it can

be

treated as if it were

a two-dimension al object,

and

this

is

what

CG cal

culations assume

(see A ppendix B .

Figure

20 Plane

of

symmetry


22/32

T

he Br

itish G

lidin

g As

socia

tion

Man

ual

Neu

trally

stab

le

Cou

ld go ei

ther

w

ay

Uns

table

St

able

aga

in

Figu

re

2 The

topp

ling

box

Fal l

in g

ove

r

Thin

gs t

oppl

e w

hen t

he

line

o

a

ction

o

f

t

heir

weig

ht

v

ertic

allydo

ward

s from

th

e

C G

goes

bey

ond

so

me

edg e

or

plac

e on t

he

o

w

hich

wil

l

act as

a

pi vo

t po

nt (f i

gu re

21

). A ba

ll

o

n

le

vel grou

nd d

o

and

can

t fal

l ove r

b e

ca us

e, bei

ng c

ircu l

ar , the

p

iv ot

poin

t

is a

l

dir

ec tly

u

nder

ne th

the

C

G

(fig

ure 22)

.

A s

far

as

th e bo x in

figure

21

is

concern ed ,

it can

be

in

one

of

b

as ic

state

s:

(1 )

Equ

ilibr

ium .

Th

e

bo xs

w

eigh

t

ac

ts

st r

aight

do w

n

th ro

ugh

midd

le

of

th e

base

.

Pos

itive

ly stab

le. T

he w

eigh

t s lin

e

of act

io n re

m ai

ns to

the

ofth e

initi

al

equi

libri

um p

osit

ion, g

iv in

g

th

e

box

a te

nde n

c

t

ip ba c

k tow

ards

it.

N

eutr

ally

stab

le . A t

so m

e po

int

th e

wei

gh ts

lin e

ofactio

n

strai

ght

th r

ough

ag

ro un

d cont

act/p

ivot

poi

nt, s

uch

as

th

e b

ed

ge. Th

ere

is

no

wt

he s

am e w

eig h

t/m a

ss

ea ch

si

de ofthe

p

Thebox

is

in

fine

balance

and

can

fall

either

way.

(4

)

Uns

tableor,

de p

end i

ng o

n

how

you

loo

k

a

t it,

p

ositi

vely s

t

T

he

we

ight

s lin e

ofacti

on

is w e

ll

to

t

he

sid

eof

th

e p

ivot

p

oin

t

pu ll

s th e

box ove

r. If

w

e

th

ink

of

the bo x

as

f

al lin

g

to

war

ds ano

eq

uilib

riu m

state

[

5], then

[4] ca

n be

se

en a

spo s

itivel

y

s

table

F

igure

P

ivot p

oint

ofba

ll

C

G

whe

n the

re s

no

G

In

ze r

o gr

avity

th

ere w

ould

be

no

C G

as

s

uch,

s

o

th

e

in -b

ala n

ce an

d

o

ut-o

f-ba

lanc

e

c

at

whi

ch we

ve look

ed w

ould

n t

seem

to

a

pply

. H ow

ever

,

t

he ob

ject

sti

ll

h

as

a cen

tr

mas s,

at th e

sam e

place

as

the

CG,

and

ev en

i

f

it

cann

ot

be loca

ted

by

any

of

th

e m

eth

pr

evio

uslyd

escr

ibed

,

yo

u

on ly

ha v

e

t

o

spin

th

eob j

ect to

r

ea lis

e

th

e i

m po

rtanc

eo

f w

you

put

th e

pi

vot .

W it

h th

e pivo

t in

the wron

g

pla

ce th e

ob je

ct ju

m ps

aro u

nd, m uc

h

as a

wa

shin

g m a

c

d

oes

if i

t is put

o

nto

th e

sp

in cyc

le whe

n t

he c

lo the

s in

side

are n

t

d

istrib

uted

e

venl

y.

ro t

atin g

o

bjec

t w

ill

tr

y to

sp

in abo

ut

its c

entre

of

mas

s, and

an y

a

ttem

pt to

mak

e

i

oth

erwis

e

p

rodu

ces

an

im b

alan

ce le

ad in

g to

the

k

in d

o

f be

havi

ourjust

d

escr

ibed.

M

o

m

e

nt

s a

nd

l

ev

er

s

Moments

and

levers

are

fu nda m ental

to

balance,

and

crucial in re la tion

to

gl ider

stab

se ech

apte

r

six)

.

M

om

ents and

le

vers

have

nt

been

m

enti

oned

in

prev

ious

sec

tions

,

th

ey ve

be

en

th er

e, b

y

i

mpl

ic atio

n.

W

eve all had

a

go

on

a

se

e-saw

.

W h

en

so

m eo

ne of

our

w

eight

sat

o

n

th e op

posit

e

(e

xa mp

le

figu

re

23).

ev e

ryth

ing

bal

ance

d ou

t nd a

jo

yf ul tim e

was

ha

dby

all.

Pu

6


23/32

efin

inevitably heav

ier p

layground bu lly on

the othe

r

end, and wh

en he sat

down

we

shot up

in

the

air (example

()). A fter a bit of

teasing, of f

he

woul

d

lea

p

and

down we wo

uld

crash

(e xampl

e (C)). The practical so

lution to this

problem

is not

a contr

act killing,

but so methi

ng

which

gives us

at

least

an

equal influen

ce on

the see-saw's

behaviour.

The m

om nt o

a

forceis its

distance

from a pivot or

fu

lcrum

multip

lied

by

its magnitude For

the

see-saw

to

balance ,

our

tw o

mom en ts

about

the

fulcrum

m

ustbe equal. At

the sa me distance f

rom the fulcrum

as ours

elves,

the bu lly had

the

greater

moment

(effect),

so we

took

off

w

hen h

e

sat

down.

If

he inches

nearer to the pivot and

we

stay put, he arrives

eventual

ly

a

t a

position

where his

moment about

the fulcrum is the

same as ours,

and the

see-

saw balances.

Alternatively,

the fu

lcrum ca n be

moved

towards

him

(exam

ple ()), whic

h pu

ts

mo

re of the

see-saw on our side

and gives

u

s

so m

e

extra

le verage

The effects

are

the

same.

A similar se

e-saw act is ne e

ded to m ove a

two

s

eat glider around

when

thepilots ar

e alreadys

trapped in. We first

have

to

lift thenose-skid of

f the

gr

ound,

otherw

ise we aren

t going to

go

anywhere

. T he us

ual way to

provide the appropriate

moment

is

to push down on the

lifting

handles

at

the

tail ine

4

in f igure 2

4. If

th

e pilot s

are

ve

ry heavy,we may

have to use most, if no

t

all

o

f

our

weight, bu

t

there is

then so

little

friction betwe

en

our feet and the ground

that

by

ourselv es we cannot pr

ov ide any usef

ul pu sh.

If the co m

bined

weight

of t

he

people

sitting

in

the

c

ockpit is

308lb (22

sto

ne ), then th

eir mutual fulcrum

is

i

2 3

t

he C G

of

their combi

ned weights

.

T hi

s acts along line 1 ,

th

ree

feet

ahead of th

e

g

lider's fu lcrum, the

wheel

(

line

2). T

he set-up is identical to

a

lm ost all the

weight being

o

n the bully's

side of

the

see-saw

(f i

gure

23

()).

T

he formula which

works outhow

hard you ar egoing

to ha

ve to

push

down on

the

tail (2), 1 1 feet b

ehind the

fu

lcrum, to

ex actly

balance

the people

in

front

, is

W

p x A

=

WY x B

or

the

left

hand

moment mustequ

al

the

right ha

nd

moment

W

hat

is

the

m

inimum downwar

d force (W

Y

need

ed

at

the

tail

to

li f

t

the

no s

e? Grit

your te

eth WY = p x

A/B,

which is

308 x 3

H

1 1 =

84lb

(6 st

on e). T

his only just

balances

the pilots w

eight, so

a

bit mor

e is

n

eeded to lift

the

glider's

skid

clear

of

the ground.

If

you push down

just

behind

the

w

ings,about

four feet

beh

ind the f

ulcrum

(3),

the balancing

force rises to 23 lib (1

6 V

sto

ne). One

foot closer

and

it

is 308lb

(22

stone)

. Sixinches from

the

pivot it is

l

,848lb, abou

t three quarter

s of a ton.

Figure 3 Th esee-saw

Fig

ure 4 R

aising

the

nose

or diff

icult?


24/32

The

British Glidi

ng ssociati

on Manual

1

units

Figure

2 5 Vectors and

their

resolution

Vect

ors a

nd

the resolu

tion

of

force

It is

not

unusua

l for groups of

people to wor

k

agai

nst each

othe

r

w h

en they

think

th e

coopera

ting, an

d

m

oving

gliders

around is no ex ception

. H o w o

ften have you seen

t

people

pushin

g on one

wing and

one

on the oth e

r,

w

ith the wing

tip ho

lder tr

des pe

rately

to

k

eep

su

ch

a lo

psided

set-up going

in a

straig

ht line?

Even

two help

ers

co mbine to

success fully

thwart

each

other s

efforts,

and

yours .

In

figure

2 5

@

w e ha ve

two such helpers.

T

he y

are very

re liable and w ill p

co

nsistently,

o

rnot at al

l.

I

n examp

le B ) , helper H

t alw

ays

pus

hes ea

stward

w

ith a f

of1

00 units (lb,

oz, kg

,

w hateve

r),

whils

thelpe

r H is set

on pu

shing

blin

dly north

a forc

e of

50

un

its. Both

w ill

act

upon the glid

er

th rough

th e

same point

w h

ere

w

heel co

ntacts

th

e

ground and the glid

er

w ill respond

to

oth

their ef

forts.

Before

t

hese helpers ev e

n

beg

in you

can w ork

out where th e

glider is

likely

to

end

This

invo

lv es

a proces

s k now

n as

re

so lution

which can b

e done either ma

thematicall

graphic

ally.

Th

e

graphical

m ethod involves draw

ing what

effect a sc a

le

m

odel of the

forces in

volved,

and uses

s

omet

kn

own

as

a parallelog ra

m of

o

rces.

Draw th

e

forces out

at

sca l

e

l

engths (1 mm = lib,

for

examp

en s

ur ing

that b

oth

line

s

st

art from

the same

point and have

correc

t a

ngle betw een

them.

C

omplete

the p

arallelogram,

mea

sure thediagon

al he

result, or re sultant.

Both the math

s

the

gra

phics say

that

w h

en

H[ pushes

the gl

ider one foot to

East, H

pushes it six inche

s

to

the

North. Their

efforts

result

r

oughly nor

teasterly

force

on the

gl ider of 1

1 l.Slb (examp

le (

Example

() s

hows Hj

and

H

actin

g

at r

ig ht angl

es to

other

, ut more

lik

ely

th

ey ll act at

some ot

her angle

. sh

th

em

bec

oming hopel

essly confused

andpushing aw ay from

other

. A

s

you

might

expect, th e useful

result(ant)

is

l

es s

before (ap

proximately

80 lb),

ut

still in a roughly

nor

th-eas

di rec tion.

In

the extreme

case

(example

()),

they

are

pu shin

comp

letely opposite directio

ns. The

resultant

is 50lb

i

n an

eas

directi

on, w it

h the helper on

the left bein

g

dra

gged ba

ckwards.

easy to see

what a desperate

ly

inefficient w ay this

is

o

f re turni

g

lider

to

the

launch poi n

t.

Graphical

re

solution becomes

m o

re

in a

ccurate the m

vector

s involve

d, and o

nly works

well for very

basic situat

where th e forc

es are neit

her too di

fferent

in

magnitu

de, n

or

alike in direction.

As a

way

o

f ske

tching outa

likely resul

h

owever, it

w

ill give

a

ro

ugh idea ofw

hat is

likely

to ha

ppen,

can

serve

as

a

useful

cross ch

eck for anyarithm

etic.

W hen hun dreds,

even

trillions,

of

small

forces are

acting

surface,

re solving

th

em

becomes

c omplicated

.

A t

sea-

pres

sures ea

ch molecule of a i

r is

abou ta

m

illionth of a m

illim

from

its nearest ne

ighbour. H

ow each be

haves is

critica

18


25/32

A

pp

B

ibli

ogra

phy

The

follo

wing bo oks a

nd

p

ublications

were re ferred to

in the writing

of this bo

ok.

OP = Ou

t

of

print

A ir Registration

Board,

British Civil

Airworthine

ss

Re

quirements

Section E , 1948

Boyne,

W

. J.,

The

Leading

Edge Arta

bras, N ew Y or

k , 1991

Bradbury

, T .

A.

M., M e

teorology

and

Flight

A

C

Bl

ack, 1989

British GlidingAsso

ciation, Sailplan

e and G liding

ma

gazine)

C AA, Joint Airwort

hin ess Re

quirements

Section

22 ,

1983

Carpenter,

C.,

Flightwise Volumes

and

2), A irlife,

1996

and

1997

Chambers

Twentieith Ce

ntury Dictionary

1976

Ch

anute, O

.,

P

rogress in

Flying M

achines M N

Forney, 1894

C

oncise

Encyclop

aed ia of Science and T

echnology 3rd

Edition), Parker

/McGraw-Hill,

1992

Crystal, D

., The Cam br

idge Biograph

ical

E n

cyclopaedia

Cambridge

University Press,

1995

Gibbs

-Smith, C . H., T

he Aeroplane an

historical su

Documents

The British Gliding Association Manual - Sample