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List 41 dtd 13 Sep 1949 per AMC-AF; AFSC ltrdtd 13 Jun 1968

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TECHNICAL REPORT Report No. F-TR-2123-ND

HEADQUARTERS AIR ScATSKIEL COMMAND TfRIGHT FIELD, DAx'TONf OHIO

CALCULATION OF TitE TEMPERATURE WHICH A PARACHUTE CANOPY ATTAINS AT HIGH ALTITUDE

Dr. E. R. G. Eckert

Restricted classification oencolled 18 months from dato by authority of Commanding Genarsl, AMC By gd£f^ifr&e&zs=i /&f9 Da comber 19U6 <w

Approved byt

Salvatore A. Mauriello, let Lt, Air Corps Propulsion Section Analysis Division Intelligence (T-2)

Approv»d byt

äUMtJUL E. N. Hall, Uajor, Air Corps Aotg Chief, Propulsion Section Intelligence (T-2)

For the Commanding Generals

Vv< <rr ***** ***•

Paul F. Hojfmick, Colonel, Air Corp» Chief, Analysis Division Intelligence (T-2)

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CALCULATION 07 THE TEMPERATURE WHICH A PASACEOTE CASOPY ATTAINS AT HIGH ALTITUDE

Dy

v -••ft

Dr. I. P. 0. Eckert

BIOGRAPHICAL ROTE

Prof. Dr. E, R. Q. Eokert is an expert on thoriaodynajnice, especially con- cerning heat transfer and gas turbinee. Proa 19*8 to l$ky he was head of the depertsent for thermodynaaice at the Institute for Aircraft Engines at the LFA In Brunswick-. In 19k} Dr. Eckert Became profoeeor and director of the Institute for Thsracdysastlos at ths UniTereity of Prague.

Is finished hie studies at the Usiversitiy ef Prague in 192? and later bs- eaas lecturer at the aass University. From l$5k to 195« Dr, Eokert vae ssniö? engineer of the angina laboratory at the University of Dansig. In 19^2 he «so lecturer at the University of Brunswick. At the LFA he vas in charge of re- search on gas turbines and jet propulsion. Dr. Eckert holds tvo degress of Doctor of Engineering.

Sis work coBprises heat radiation; heat transfer, especially at high ve- locities! research on Jet propulsion and gae turbines, especially that concern- ing high temperatures; ooabustion probleas; flow investigations on turbine blades «»ploying the optioal Interferometer; and heat exchangers for gas turbines.

Ee is now («ployed in Propulsion ssafcion, Analysis T-S, AMC, Wright Field, Dsj'toa, Ohio.

Division.. Intelligence

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TABLE OP-COKTENTS

it Ir»vS?öduetiön , i • i • r • • • • • .-•..-•-•-.-... •-•-•-• •-•=.-• ..i-..•• •.••• •;• • • •."•.• • • 1;

2. Inhärent Teapersture and Heat Transfer by Convection .... 1

4. CtlouUtion of Surfte« ftaperatur» .......................... U

5. Numerical Cilöülttiohi- • -.. .-•.... ->-. • • •-=.-•=• .*.....•••••••• • £

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CALCULATION 07 THE TEMPERATURE WEICH A PÄPACHUTE CAHOPi ÄTTAIHS AT HIGH ALTITUDE

by

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Dr.. E. B, ö, Eckert

BIOOSABHICAL SOTS

Prof. Dr. E. B. Ö. Eokert is an expert on theraodynaBioe, especially oon- oerning b»at transfer and gas turbines. Prom 1936 to 191*3 he was tiead of the department for thermodynamics fit the Institute for Aircraft Engir.se at the LFA in Brunswick. In 191*5 Dr. Eokert became professor and director of the Institute for Thermodynamics at the University of Frague,

He finished his «twdies at the University of Prague in 192? and later be- came lecturer at the sea» Jtoiveraiiyi from-. I9|!»to. :i93B"Dr. SeSsrt wae senior engineer x»f. the engine laboratory at Sb* pörfr'SjDty- -at-;Dänsig. In 19^2 he- was lecturer at the University of Brunsviöfc. At the LFA he vae in charge of re- search on gas turbines and Jet propulsion. Dr i Eckert holds ivo degrees of Doctor of Engineering.

His work comprises heat radiation; heat transfer, especially at high ve- locities; reMarch en jet propxilaion and gas turbines, especially that concern- ing high temperatures; bonbustlok problems; flow investigations on turbine blades employing th« optical interfero&eterjand heat exchangers for gas turbines.

T-2; He is now employed in Propulsion Section, Analysis Division, Intelligence AIT, Wright field, Dayton, Ohio.

-TH-2123-3fi> i

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TABLE OP CONTENTS

-P«g* 1. Introduction ,...,.....,.... * J;S:,;.,...;;;.^£s...........• »*•-. 1

2. iftS§i"*.Jit Teap«r^tuj?.fet^LHAti;,Tc*n|if.»r fey Convection••*.-..$ 1

3. Heat Exchange by Radiation .....-.........,...?«............ 3f-

k. Calculation of Surface Te»perature ...-...................... U

5. Nuste.rlosl Calculations .......................;........,..--... 5

v. References . ..^.^s-»-.'.-.-»"..v-.. • •. .'O

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CALCULATION ÖS-THE TEMPERMURE'WHICH'"A" PARACHUTE CANOPY ATTAINS AT" HIÖH ALTITUDE

1. Introduction

Since at high altitudes the air density is very low, a paiachute descends With • very high speed. Therefor«, relative to the parachute, the air moves with «reat velocity. In the boundary layer, whichr-biiiTdih-üp iiong: the surfaces of the iparaohut«, and in th* wake oehind: it, the air is decelerated .and iti- klnetic energy is converted into heat. Thus- the parachute is heated: .upv but.,, on.the other hand, it radiates heat into the universe and to- the earth. During the day it also absorbs solar heat radiation. The temperature which the canopy attains under all these influences is calculated in-, the. following paragra.phiV

2. IhBg'rent Temperature and Heat Tramfer by Cohvectibn

In a high-velocity .gas. stress a body which loses newest by radiation.at-? tains an equilibrium temperature higher than the temperature 7* which is in- dicated %. s thermometer moyi.„3 along with the -stream. This temperature of the> body is ceiled its '"inherent." 'temperature-, it. can be calculated fey the follow- ing formula:

t<<

Tä-^+ * \t:

7g inherent temperature of the body

Tfi static temperature in the ga» stream (atmospheric temperature)

Y velocity of the gas stream relative to the: body

& gravitational constant

Cm specific heat of gas at constant pressure •-

y mechanical equivalent of heat

<f noridlmensiohel factor

°R

OR:

ft/arc

ft/ sec2"

BTU/lb *R

ft Ib/BTÜ

For air the denominator 2 g Cptf has the value l2j^**2/>*e2 % _P^._ faster «y depends On frii Ifiilpi of ehe sSäf. For • »«••Bislinca sway in «ri «iVr stfts» it is & « 0.85 - 0.90, for a cylinder in a flow normal to its axis & » 0.5 • Ö.7.. (Ref. 1). in eh; air" stress 0* never can be greiter"than^l.

No measurement« are known for a hesispher» with its opening: against the wr|ii§, which shape should correspond to the parachute canopy. Since we are interested in the higfieat temperature of the canopy, we may, therefore, calculate &it{i the

.r i"

F-TR--2183-ND

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V-^Jtt> -r.:—5?

t

value Ö* * i» which gives an; upper -Hält.

If the temperature of the body 1» lower than 'the inherent temper«tur* (e.g'., by radLatiorij, a continuous flow of heat streams from the boundary to the body» given by fche• ,föi'auia-j-

7'

<t«-*U*T8 -11 -Qc d?lpw of heat by~eohvectlon

At heat transfer coefficient

,-/^; .surfäse of the.: body

47i inherent tempjrature; of the body

Tr surfsee temperature of the body

(2)

BTU/hr_ft2 <>R

0R

By calculation Ina experimentation it was proved that) for streamlined bodies, the heat transfer coefficient does not. depend materially on the Mseh number, so that formulas derived by experimentation with low velocities can also -be applied' to< supersonic flowi (Ref.. 1). In supersonic flow, the, velocities along the surface are decreased by shook waves arising in front of i-blunt body. Again, no experiments on shapes similar to ä ptrschute canopy are known, so we mast use -formulas of. other bodiee;. We. shall use the results from tests on spheres., fhey can be expressed by the formula (Rsf.-24.

i-

I";. i:-

4 1

«0.33 I ML4 (K6r (3)

diameter of the sphere

heat conductivity

y kinematic yisoösity

ft . •

BTU/ft hr n

ft2/sec

— II It expected that the heat transfer from 'the wake to the rear of a hemisphere representing the" -parachute- canopy is approximately the seme as the hefct transfer on the rear of the sphere. The heat trafisrer bhrthe in^r-sj^fioe. of the hemisphere is certainly smaller than the heat transfer on the front lielf of the sphere. If we calculate with formula 3 for the parachute canopy, we get values too high for the heat flow fro» the air to the parachute canopy, and therefore an upper limit for the surface, temperature,,

Til* perms»oiitty u? •#- >.K»..»iaat. t-SSSSf-lr;!-

So we cheek our results by calculating the Heat flaw; in a different way. It if»« proved by »xpepimehts that, the: volume; of sir v in qu ft, leakftig through one sq ft of the parachute cloth per sec increases linearly with th« ppessurf diffe?jj?9» A P on both sides of the cloth. On the other hand., dimensional analysis requires

F-TR-2123-BÖ

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that i relationahip

'T-rt J>* f fc*fe) m

exjlst .( ^ specific: weight, öf tip:)., If we build up the Reynold» Nö. Re with the porosity v* (which has the dimension of • velocity), the diameter. D of thas^pa- chute canopy, and the dynamic yiiiqosity **• of t-hs air { Re * #jjj?ty» we g»t_a lineir d*psRdsr.cy bstwssn= vli« pf*ssu?e <3ifföFene* ö j* and the porosity v in <j «•only If /$&}'•

This results in

n

Ths formula ihöwi that the porosity dees hot depend on the air density. Ther*= fore/, we peh=use the results e£ ssp;»ris§eLta it normal pressure, for the descent; at high altitude also.

Now we :may assume that this air lecking through the canopy is; cooled down 'i t?or-s" ^1} to the^ »j»rface temperature T. of r-lc" " "•- *••- -

from the inherent tempera ture= T. ftur-••& the canopy. This gives a heat flow C^ to the canopy

- .*•'!

II

! (

; 1 <

Qc= £-CfV(Ti-% (5)

the factor 1/2 arises because in A both sides 0? the canopy surface are included.

It la proposed to calculate, with formula 2 0? 5, which of the two gives higher,valüea for the heat flow Qfl. The porosity of normal parachute ^loth is 1.3 ft^/ft^sec. In the example calculated in paragraph 5, the heat flow cal- culated with eq. 2; becomes approximately twice as great as that calculated with eq; 5. Therefor? eg 2 was used for the final; oomRutatierts.

3... Heat Exchange by Radiation

The parachute canopy radiates heat to the universe and to the earth and en the other hand absorbs heat radiated from the earth and from the sun. At long as the altitude is small compared with the .diameter of the earth» the inner part of the surface.A of the parachute canopy exthalgeii heat by radiation practically only with the earth; This gives the formula:

Qn> - eA?«C$-$?) (6)

vfffi «Ms?r?h«sech«xig« by radiation between parachute and

/» area of projection of parachute on a horlsontal f\P*- plene

Bfü/hr

ft2

P-TS-S123-1TO

/

*«tts (7)

i.--2- The ioltr radi»tiqh it high tltitujjfti: on, 1 ,ft area normal tö thi sah "ray» **•-§&; • f 25 .fflD/ft?!» ijpi... ^ i-; tRs: prsjsetivn; ST tne s«rachut« in this direction, the solar radiation abiiorbed by, the parachute ir

'Qj. * OC Mptt. Q»A. (8)

The projection area is aexisus when tht sua is vertically »boy«; the parachute. To get an upper limit for-the'i surface temperature,, the aa«a value of Ä y»*.aa in Bq 6, namelythe proJedtiiin-Von^i horlsontaT pane has= to be used. ;

The absorptivity PC for sun radiation; depends very muoh en the color of the parachute, »or white cloth It is app?0J5Ö«it*ly ofc -0,2, for dark cloth it «Sy increase to almost 1

•f. Calculation of Surface Temperature.

Now the suvfaoe temperature nay be calculated by a heat balance. During the -des'senti the temperature of the peraehüte ohangee oohtinuausly. The hest stored in the material of the parachute per unit time is:

9AP&*fr7*&Y m

:!«•- ». l-l- I

£ emissivity of parach te iurfaoe

-C*. 3tefan-BoJ|Banh ooMitni 0,1?1* 10"^:

Te temperature of earth

?hr •**•

Since a part: of the radiation «Bitted by the inner surface strikes other areas of this sane surface and is absorbed by it*.-only the projection are» A

•jvttfn a horizontal plan? is ismsted in Bq 6. The essentiai part of t-he radiation at the temperature* the canopy attains» Ties in the Wave-length rang* between 2 and 10J* . For these wave langths the emissivity of all eiectricti nonconductors is £ =0.80 1.0. The color of the surface doea not influence this value.

The upper half of the canopy surface exchanges neat by radiation with the universe. Since the temperature of the universe is 6 °R, the second term in Bquatiön 6 yinlshes: tnd the h*§t flow is Jiyfh by

• I.

F-TB-2123-HD

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A. thickness of tht parachute cloth

")f epeoific weight.paraohutt cloth

C «pacific heat paraohutt cloth

V **•• # attitude

ft

lb/«»?

BTU/lb «F

sec

ft

In tht ftboya f©raula the »mall temperature differences Within tht para- ohutt cloth are neglected. Mow th« heat balance givee!

If ths Mat storage In the parachute material can be neglected, ths left- hand term becomee sero and the surface temperature T may'be determined from

^^e^^xu^^^+oc^^+e^c,^ (u)

Since the heat storage in the canopy decreases the temperature variations during the descent, Eq 11 gives the highest temperature possible,

5. Numerical Calculations

Per a parachute descending, from 100. miles iilfeibüde with.-the. velseitles (Ref. 3) given in Pig, I, the -eurfae« temperature» • are calculated with Eq 10 end 11; The following values were iiseex

0.8; *-0.2'.(white cloth).. %*"* l&'> If " #•?

lb/ft/ ; e • 0;3 BTU/lb-°P.;; A. *= 0,01 in> The temperature of the atmosphere are recorded in Pig. 1; the temperature of the earth was asaumed to be. 'ffg

The property values for air are given in the following table:

Air -tBWP'erBtur'e °P T - -58° 32.° .122» 212» 3?2«

Thermik cöhq'uc'sivity BTÜ/hr ft ^P 0.0134 Ü.0159 0;0182 0.020ft 0^021»!

JU«:l._l.M-._.-1.99- 2-.A6. -SvtfT. Kinematic viscosity,IQ^f t2/sec 2.-56. TIT r -

The kinematic viscosity is given for normal pressure^*JI . It must be multiplied, with the ratio of the normal pressurey«n to the. pressure••M. to get the value for pressure -/a. . '-'

P-TR-2123-KB

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,sa

_u

I 2 fj

i-^iS?- .-- n*r

;-

The results of th8 calculation are presented in Pig. 1.

At altitudes «feave 60 »litt the convective heatHrtaafer eoefficient ^=%^rol^TsriBoünSti^is^2^1stcoa^-so^9M}/i-btoauee-of- low:.ale- =ä«ri«ity that the surf toe temperature is detrained only by the exchange^ ©r radiMed heat.

The curve t^ gives the surface tempefciture of the canopy, if the heat storage is neglected (according to foraula 10); curve t represents the surface tempera tüst>e talcing into account the heat storage. The second curve ma eeleulaied from equation 10 by isoclinal Method. It can be seen that the differences between the two temperatures ti and t8 are small. The highest Jeaperatur* |312e?} occurs at 37miles altitude, where the convective heat transfer is already great and the velocity still high.

This-näxlBusi temperature was- also calculated for a canopy of dark" cloth. ( «. • Ö.8). A value of 3itOeF was found.

6. References

1« E.R.O. Eckert:

2.

3.

W. H, HeAdams:

"Heat transmission of Bodies in Rapidly F?.owln* Oases.' frssress,.Report Mo.- -M IRE 46 (19U6).

"Heat Transmission/" 2nd Ed; KcOraw-Hiilj Mew-York, 1942 p. 237;:

"Considerations on the Descent of a Parachute from High Altitude, by E. L. Chambr* and Pi t. Nalina - California Institute of technology/ r 30 April 1'946.

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