AIAA Student Competition 2015 Research Paper

American Institute of Aeronautics and Astronautics

Interference Drag During Store Separation

Kalendrix Cook1, Michael Halvorson2

Students, Department of Aerospace Engineering, Auburn University, Auburn, Alabama 36832

Interference drag is generated when bodies placed in a uniform flow are in close proximity. Tests

were conducted on two axisymmetric bodies placed in tandem at different horizontal and vertical

spacing to represent stores separating from a combat aircraft. Forces were measured in a wind tunnel

with a six component force/moment sensor at three Reynolds number. Data showed strong

correlation between the measured forces and spacing between the two bodies, however the forces

remained largely insensitive to a change in Reynolds number until reaching a threshold. Key features

of the flow are discussed and presented.

I. Introduction Since the 1940’s, aircraft carried stores such as bombs, fuel tanks and other deliverables on the exterior that

results in a very complex flow field between the stores and also between the stores and the mother ship. The fluid dynamic interactions manifest themselves in the form of interference drag. It may be noted that due to the interference, the total drag of an aircraft, including wings, missiles, etc. is often greater than the sum of the drag of each individual component.3

Figure 1: Interference due to stores

Because of the proximity of the stores protruding from otherwise smooth underbelly of an aircraft (Figure 1), highly turbulent flow consisting of large and small eddies is produced. At high speeds, pockets of localized regions of sonic or supersonic flow results in the formation of shockwaves that alter the pressure distributions and impose additional unsteady loads. Release of stores under these circumstances results in changes in trajectory, targeting error, collisions between stores and in some cases, released store returning to hit the carrier aircraft. Possible impact between a released store and fuel tanks pose serious hazard. For the stores released from internal weapon bays, weapons traversing a shear layer undergo high amplitude oscillations. Whether external or internal mounting, both methods have relative merits4.

For stores mounted in tandem, interference between the wake of the upstream store with that of the forebody of the store downstream is a challenging problem because of the vibrations and aeroelastic coupling. The objective of the present work therefore was to investigate the interference drag of two axisymmetric bodies mounted in tandem.

1 Undergraduate Student, Aerospace Engineering, 211 Engineering Dr, Auburn, AL 36849, Student Member 2 Undergraduate Student, Aerospace Engineering, 211 Engineering Dr, Auburn, AL 36849, Student Member 3 Asselin, Mario,” An Introduction to Aircraft Performance,” AIAA Education Series, 1997, Chapter 1, 24. 4 Johnson, Rudy, “ Store Separation Trajectory due to Unsteady Weapons Bay Aerodynamics”, AIAA Journal, Vol

46, No. 188, January 7, 2008, pp. 2008

2


II. Description of Test Equipment and Procedure

The test was conducted in a 2ft x 2ft, open circuit low speed wind tunnel. Test were conducted at freestream

velocities of 30 fps, 60 fps and 90 fps resulting in the Reynolds numbers of 39,000, 78,000, 128,000 based on the

diameter of the model. Two identical missile models were constructed from modified Este’s model rocket kits that

had a plastic nose cone and cardboard body. The 2.5 inch diameter model had an overall length of 8.0 inches. One

model was equipped with a load cell and the second model was filled with foam and mounting hardware. A special

adapter was designed to hold a load cell inside the model through a L-shaped mechanical linkage that was mounted

to a two axis traversing system placed on top of the test section through a horizontal slit. Thus the model carrying the

load cell could be easily traversed horizontally and vertically. The “dummy” model was attached to the ceiling with

selectable spacers of one, two and three diameters. These spacers were enclosed in airfoil shaped streamlined tubes to

minimize support interference. The test setup and the coordinate system are presented in Figure 2.

The force/moment balance used in this investigation consisted of ATI Industry’s ATI9105-TW-NANO25 sensor

capable of measuring forces and moments in orthogonal planes. Maximum axial load for this sensor shown in Figure

3 is 25 lbs. that was well within the range of forces anticipated. The load sensor was calibrated before each series of

tests to measure any possible drifts and noise. Data was acquired with a National Instruments A/D board and Labview

software. Sampling rate was kept at 500 Hz

Tests were conducted for a variety of configurations consisting of the setting anterior model where 𝑍

𝐷= 1 and

moving the posterior model axially downstream from 𝑥

𝐷= 0.4 to

𝑥

𝐷= 2.8. Forces and moments were also measured

without the anterior model. The experiment was repeated with anterior missile positions where 𝑍

𝐷= 2 and

𝑍

𝐷= 3. The

baseline measurement consisted of the posterior model alone and was used as a reference for comparison with the

cases with interference introduced by the presence of the second model.

III. Results and Discussion

Drag and moment coefficient data was reduced from the collected data and tabulated. The goal of the experiment

was to determine if any pattern existed between interference drag and the relative vertical 𝑍

𝐷 and horizontal

𝑥

𝐷 positions

of two models in tandem and to provide possible explanation of observed changes. The data plotted in graphical form

therefore represents the changes in drag and moment coefficients for each configuration. Tandem bodies in high

Reynolds number(Re) flows experienced significantly more interference drag fluctuations than at lower Re flows,

however the drag coefficient magnitudes for high Re flows were closer to zero. While the drag data shows obvious

changes in the posterior model’s stability, the primary reason for separated store collision is the changes in the location

of the center of pressure that contributes to the random motion of the store.

The situation is aggravated because of the separated flow between two bodies in tandem. Without proper store

release orientation, a large, unanticipated moment is therefore introduced on the store. By separating a store in tandem

with an interfering body at a designated orientation, a mother ship could intentionally mitigate the viscous effects

inherent in interference drag. This task is done quantitatively by integrating the total moment interactions on the store

across its vertical and horizontal translations. A combination of drag and moment analysis for a flow system can lead

to a mathematical pathway for the store’s motion sufficient for it to gain self-imposed stability.

Positive axial drag on the posterior model experienced a linear increase in magnitude with increasing Re for all

relative distances 𝑍

𝐷. This result is consistent with a change in viscous force ratios. The axial drag coefficient function

patterns did not change with an increase in Re, and the drag coefficient elasticity per interval varied only slightly for

higher Re flows. Figure 16 shows the axial drag coefficient data for 𝑍

𝐷= 1. The small or negative drag coefficients

where 𝑥

𝐷= 0.4 are due to a drafting effect in which the close proximity of the of bodies leads to a sharing of laminar

flow properties. As the relative distance 𝑥

𝐷 increased, the wake from the upstream model was no longer laminar across

the forebody of the posterior missile. The flow across the anterior model’s back face became turbulent or separated,

and the posterior body caught in its wake experienced a steady increase in axial interference drag until a maximum

value where 𝑥

𝐷= 1.6. The imposed interference drag incrementally subsided with further increase in store separation

𝑥

𝐷. For the Re=78,000 flow, the drag coefficient caused by the anterior model was near zero for the duration of the

store separation displacement.

3


The moment diagram for the axial torque is located in Figure 19. The values were consistently near zero. The

models were oriented a sufficient distance away from the wind tunnel walls to preclude any wind tunnel boundary

layer perturbations, and very little flow vorticity was measured.

For the relative distances 𝑍

𝐷 = 2 and

𝑍

𝐷= 3, the magnitude of the axial interference drag for the Re=128,000 flow

was half or lower than what it was where 𝑍

𝐷= 1 for the majority of relative distances

𝑥

𝐷. Figures 17 and 18 depict the

geometrically similar drag coefficient patterns with the maximum drag occurring where 𝑥

𝐷= 1.2 . Both relative

distances 𝑍

𝐷 showed a drop in drag coefficient magnitude where

𝑥

𝐷= 1.6, and the drag magnitudes displayed little rate

of change for the remainder of the increased store separation. Where 𝑥

𝐷= 1.6 was the lowest interference drag

magnitude for the relative distance 𝑍

𝐷= 2. Again, the drag coefficient was at a maximum where

𝑥

𝐷= 1.6 at the

𝑍

𝐷= 1

configuration. This shows that as the anterior model descends it produces not only focused areas of flow interference,

but also focused areas of little or no axial interference. These measurements are what can be qualitatively used to

locate the positions most conducive to interference drag mitigation on the posterior store. This description holds true

during interference drag coefficient analysis for each axis.

The axial moment diagrams for the two relative distances 𝑍

𝐷= 2 and

𝑍

𝐷 = 3 are located in Figures 20 and 21. The

torques measured for all store separations 𝑥

𝐷 were also near zero values, and therefore interference drag is not

considered to create significant flow circulation.

Each of the drag coefficient values measured for the posterior model’s vertical axis was negative. Figure 10

through 12 represent the drag coefficient data taken on this axis, and all three of the relative distances 𝑍

𝐷 displayed

sinusoidal drag coefficient patterns with increasing store separation. Where 𝑍

𝐷= 1 neither the magnitude of the drag

nor the function’s sinusoidal amplitude increased significantly with Re. The vertical interference drag across all store

separations displayed small standard deviations, implying a stable but negative vertical environment for coaxial

bodies. This result is corroborated by the moment diagram in Figure 13. Upon release at 𝑥

𝐷= 0.4, the posterior model

would experience a significant negative moment about the y-axis, or a downward pitch. As the model’s store

separation is increased, the moment coefficient about the y-axis emulates a parabolic function and becomes positive

by 𝑥

𝐷= 1.2 for all numbers Re. This observation states that for coaxial bodies traversing store separation at all values

Re, the resulting vertical center of pressure changes location with increased relative distance 𝑥

𝐷.

The vertical drag coefficient patterns for the relative distance 𝑍

𝐷= 2 exhibited a sinusoidal behavior at negative

values, however the amplitude of the function was more proportional to Re than where 𝑍

𝐷= 1. Drag coefficient

magnitudes at all values of Re experienced local maximums at 𝑥

𝐷= 0.8 and

𝑥

𝐷= 2.4 and local minimums at

𝑥

𝐷= 0.4

and 𝑥

𝐷= 1.6. The drag and moment coefficient diagrams are located in Figures 11 and 14, and the rapid change in rate

direction is apparent in both. Until reaching store separation 𝑥

𝐷= 2.0, the high Re flow at relative distance

𝑍

𝐷 = 2

exhibited the lowest magnitude of all measured vertical drag coefficients. This observation points to a drag pattern

whose sinusoidal amplitude has an inversely proportional relationship with Re. Conversely, the moment coefficient

data displays a directly proportional with Re. These considerations must be taken into account when designing a high

Re flow system. The vertical drag coefficient magnitude would be low for all measured store separations, but the

moment coefficients would experience large shifts in value magnitude and sign. A highly negative vertical drag

coefficient is not usually a desired result, but if a moment magnitude is too high to sufficiently mitigate after

separation, then the store will no longer be oriented in tandem with the interfering body.

Because the flow propagations occur below the model instead of around it at relative distance 𝑍

𝐷= 2, the wake

oscillations more frequently shifted its center of vertical pressure. At store separations 𝑥

𝐷= 0.8, 1.2, and 2.0, there

existed peak relative distances of significant torque application to the store. Each of these points poses serious hazard

to store and release body integrity if the store is left under that particular configuration for too long. To mitigate the

uniformly opposing nature of the pitching moments, the store need only pass through both areas at a constant rate. By

utilizing this constant separation rate technique, a store with axial translation could keep its center of pressure within

a manageable range until it gained control of its momentum independently. Additionally, a store could be intentionally

released in a non-traditional orientation that would negate any expected torque values for initial store separation. Such

calculations require extensive knowledge of the interfering body’s wake field per system.

4


For the Re=39,000 and 128,000 flows, the vertical drag coefficient function for the 𝑍

𝐷= 3 graph can be compared

to the 𝑍

𝐷= 1 function as a geometrically similar function with a higher frequency. The flow axially leaving the anterior

model caused areas of high and low dynamic pressure behind it. This directly caused an increase in negative drag

coefficients and a mirroring of previously evaluated flow data where 𝑍

𝐷= 1. Figures 12 and 15 show the drag and

moment coefficient data for 𝑍

𝐷= 3. The Re=78,000 vertical drag coefficients for this relative distance

𝑍

𝐷 exhibited an

absolute minimum magnitude of -0.958 where 𝑥

𝐷= 0.4 and an absolute maximum magnitude of -1.437 where

𝑥

𝐷=

0.8. It then gradually declined in drag coefficient magnitude with increased store separation.

The moment coefficients for relative distance 𝑍

𝐷= 3 appear similar and opposite to the

𝑍

𝐷= 1 values, but because

of the center of pressure inconsistencies at higher store separation displacements, the two should not be regarded as

mathematically relatable. The moment data’s behavior cannot be described as sinusoidal, however the magnitude of

the measured torques did increase with Re. The Re=39,000 and Re=78,000 flows exhibited a maximum value where 𝑥

𝐷= 0.4 and then lesser magnitudes throughout the rest of the store separations. Torque sign changes were evident in

higher relative store separations, but the magnitude of the moment coefficients is near enough to zero that they did not

pose significant hazard to the store’s stability.

The Re=128,000 flow began at 𝑥

𝐷= 0.4 with an absolute maximum moment coefficient magnitude and value of

0.0413. It then linearly regressed to an absolute minimum value of -0.0294 at store separation 𝑥

𝐷= 1.6. Where

𝑥

𝐷=

2.0 it reached a near-zero positive moment coefficient and then moved back down to a strongly negative coefficient

at 𝑥

𝐷= 2.4. These rapid moment fluctuations are important to note in flow design, but the most important moment

analysis result for the pitch axis is the massive difference between the moment coefficients where 𝑥

𝐷= 2.0 for relative

distances 𝑍

𝐷= 2 and

𝑍

𝐷= 3. In this experiment’s example, the anterior model’s 2.5 inch negative vertical translation

from 𝑍

𝐷= 2 to

𝑍

𝐷= 3 caused a -0.04388 shift in the moment coefficient for this store separation value from 0.0504 to

0.0065. In this comparison the dichotomies of harsh and stable flow environments during interference drag are most

apparent. If a pathway conducive to interference drag mitigation during store separation is to be found for a system,

the orientation of the store’s release must be engineered to direct it through these relative distances of least moment

coefficient interference.

The change in lateral drag coefficients must be separated into high and low Re categories due to the distinct

differences observed between flow regimes. This is only true for the drag coefficients; the moment coefficient data is

shown to have a positive linear correlation with Re. The Re Line will be defined as the Re at which the lateral

interference drag affecting a separated store adopts a different, observable behavior function than it exhibited at Re

flows less than at that point. The difference is best described as a sudden increase in drag coefficient function amplitude

and frequency. This experiment’s Re Line was evaluated near 100,000, but precise Re Line evaluations require

iterative numerical processes with a more accurate measurement devices. This number is an estimate developed from

the presented data, and the actual Re Line for lateral interference drag Re categories should be regarded as a dependent

variable per system. Low Re flows will describe the flows measured beneath the Re line, and high Re flows will

describe the flows measured above the Re Line. The high Re flow behaviors have not been observed to revert behaviors

with further increase in Re.

All of the lateral interference drag coefficients for low Re flows were negative values. Figure 4 depicts the drag

coefficient data where 𝑍

𝐷= 1, and the aforementioned difference in flow behavior per Re is apparent. The low Re drag

coefficients exhibit mildly sinusoidal behavior while remaining negative, indicating expected lateral oscillation in the

flow. Until reaching the Re Line, the low Re drag coefficient function’s amplitude is directly proportional to Re. A

local minimum magnitude is reached where 𝑥

𝐷 = 1.2, and local maximum magnitudes are found where

𝑥

𝐷 = 0.8 and

𝑥

𝐷 =

2.4. The lateral drag data shows the posterior model to be caught in the anterior model’s negative wake with fluctuating

strength per Re. The models were coaxial in this configuration, so a distinctly stronger wake direction, in this case

negative, on the posterior model forebody is not an alarming result. Upon reaching the Re line, the flow is moving too

fast for the wake to adequately affect the streamlined body, and a new behavior pattern is adopted.

The magnitudes of the lateral interference drag coefficients for high Re flows where 𝑍

𝐷= 1 were considerably

smaller than the low Re drag coefficients at all store separations 𝑥

𝐷. This generalization holds true for all relative

distances 𝑍

𝐷 except for two local minimum values at relative distance

𝑍

𝐷= 2 where

𝑥

𝐷= 1.2 and

𝑥

𝐷= 2.4. The high Re

5


flow where 𝑍

𝐷= 1 experienced a maximum magnitude and minimum value where

𝑥

𝐷= 0.4. This result shows a large

negative wake bending around the back of the anterior model. Each Re flow felt almost exactly the same drag

coefficient at this store separation. As store separation increased, the drag coefficients for the high Re flow became

positive until a maximum value where 𝑥

𝐷= 1.2. The drag coefficient then reverted to a small negative value where

𝑥

𝐷= 1.6 and remained there throughout the further increased store separation.

The moment coefficient analysis for the store separation where 𝑍

𝐷= 1 is characterized by a sinusoidal function

whose amplitude is directly proportional to Re. The moment diagram found in Figure 5 shows the store experienced

a local maximum in torque where 𝑥

𝐷= 0.4 and

𝑥

𝐷= 1.6 and a local minimum where

𝑥

𝐷= 0.8. The lowest moment

coefficient magnitudes for coaxial bodies in tandem were found where 𝑥

𝐷= 1.2 and

𝑥

𝐷= 2.4. These will be important

relative distances in the final data results and conclusions. The front and back end of the coaxial store separation data

in this Figure oppositely mirror each other in shape and pattern. The values of the back end are lesser in magnitude,

suggesting a damping term in the observably repeating moment function. This damping term affects not only the

magnitude, but also the frequency of the lateral moment coefficient function. Further research into a dependent lateral

moment function could yield an adjustable damping term used to augment the stability of the system, possibly leading

to a decrease in the locational instability on the center of pressure.

The drag coefficients where 𝑍

𝐷= 2 exhibited an inverse pattern relationship with the

𝑍

𝐷= 1 values across all store

separations 𝑥

𝐷. Lateral drag coefficients for

𝑍

𝐷= 2 are found in Figure 6. Comparing Figures 4 and 6, a negative

relationship exists between the rates of the drag coefficients until where store separation 𝑥

𝐷= 2.4. The observed

directional opposition suggests that as the anterior model descends, its lateral flow characteristics also exhibit a

measurable, vertical, sinusoidal function until the flow redacts its unstable wake characteristics upon increased store

separation and begins to re-adopt the wind tunnel flow direction. For low Re flows where 𝑍

𝐷= 2, the maximum

magnitude existed where 𝑥

𝐷= 1.2 and the minimum existed where

𝑥

𝐷= 2.0.. Two local maximums for the Re=128,000

flow existed where 𝑥

𝐷= 0.4 and

𝑥

𝐷= 2.0, and two local minimums existed where

𝑥

𝐷= 1.2 and

𝑥

𝐷= 2.4. The maximum

where 𝑥

𝐷= 0.4 was the highest recorded lateral drag coefficient at 1.236.

The moment coefficients for this configuration were significant and positive for all store separations 𝑥

𝐷 except

for a special case where 𝑥

𝐷= 0.8. The substantial positive yaw depicted in Figure 8 for all store separations but

𝑥

𝐷=

0.8 is likely a property characteristic of the wake. Looking back at the drag coefficient data, the low Re drag is entirely

negative and the high Re drag shifts in sign. To maintain a positive yaw, the negative, lateral, low Re drag forces must

have a resultant vector concentrated on the back half of the missile model. The changing, negative drag forces for high

Re flows must also be concentrated on the back half, but the positive drag forces must result in the model forebody.

This moment analysis is consistent with the oscillating lateral flow pattern described for the 𝑍

𝐷= 1, coaxial drag

coefficient data. Where 𝑥

𝐷= 0.8, the magnitudes of all Re flows approach zero.

The lateral drag coefficient data for 𝑍

𝐷= 3 does not deviate from the lateral patterns inherent in flows of lesser

relative distances, 𝑍

𝐷. The data is graphed in Figure 7. The low Re flows, with wholly negative values, exhibit a

maximum magnitude where 𝑥

𝐷= 1.6 and a minimum magnitude where

𝑥

𝐷= 0.4. It should be noted that for the

Re=78,000 flow, where 𝑥

𝐷= 1.6 showed the largest negative value measured for all lateral drag coefficients at -1.490.

The high Re flows similarly experienced rapid intervals of rate and sign where 𝑍

𝐷= 3. The local maximums existed

where 𝑥

𝐷= 0.4,

𝑥

𝐷= 1.2, and

𝑥

𝐷= 2.0. the local minimums existed where

𝑥

𝐷= 0.8,

𝑥

𝐷= 1.6, and

𝑥

𝐷= 2.4. Because of

the constant shifts in direction sign, the lateral drag coefficient magnitudes are closer to zero than previously observed

flows.

The moment coefficient analysis for the store separation where 𝑍

𝐷= 3 is characterized by a quasi-sinusoidal

function whose amplitude is directly proportional to Re for the Re=39,000 and Re=128,000 flows and a parabolic

function for the Re=78,000 flow until where 𝑋

𝐷= 2.0. The change in moment coefficient function is likely due to a

change in flow oscillation properties with increasing Re whose frequencies at higher Re values realign with the

6


patterns described in low Re values. Figure 9 displays the lateral moment coefficient data for 𝑍

𝐷= 3. At all Re flows

the calculated values were negative. The flow function shift is most apparent where 𝑥

𝐷= 1.2. An increase in moment

coefficient is exhibited for the Re=39,000 and Re=128,000 flows, but a decrease in torque is shown when Re=78,000.

The Re=39,000 and 128,000 flow models experience a significant jump to a larger moment coefficient magnitude

while the Re=78,000 flow data experienced a marginal decline in magnitude along the interval from 𝑋

𝐷= 1.2 to

𝑋

𝐷=

1.6. Each Re flow then expresses a local minimum magnitude where 𝑋

𝐷= 2.0 before ending their data measurements

in an increasingly negative direction. This data also points to localized pockets of strong interference drag and

localized pockets of tame force and torque applications. .

The lateral drag and moment data expressed a visible pattern in the flow oscillations.. For relative distance 𝑍

𝐷 =

1 in Figure 4, there are two shifts in value sign along store separation 𝑋

𝐷. For

𝑍

𝐷 = 2 in Figure 6, there exist three changes

in value sign. For 𝑍

𝐷 = 3 in Figure 7, there exist three changes in value sign, but the rate of drag coefficient change

shifts four times. This correlation directly indicates that with increasing relative vertical distance ∆ 𝑍

𝐷 from an

interfering body to an affected one, there is a rise in the frequency of flow direction oscillation in high-Re flows. This

tandem flow interference pattern can be utilized when designing store separation systems. As the separated store

descends with the constant negative drag coefficient values, it experience several changes in force directions in the

oscillating flow. If descending in high Re flows, its total integrated lateral drag coefficient stays closer to zero, but it

becomes increasingly difficult to predict in which direction it will end due to the wake oscillations. If a carriage was

to release a store largely dependent on lateral stability, the most effective method of store separation from the

interfering anterior body is to begin the separation with a large rate of negative vertical translation followed by the

store’s own capacity to guide and direct itself. The majority of stores released without the capability to orient

themselves are not traditionally placed in and tandem separation system.

The defining factors in determining the center of pressure during interference drag for bodies in tandem are known to

be the lateral and vertical interference drag coefficients. Because of the distinctly smaller magnitudes of these drag

coefficients during high Re flows than low Re flows, designing a store separation system optimized for high Re flows

would be significantly easier than designing a system optimized for low Re store separation. The optimal position

where a separated store experiences the least amount of interference drag is a configuration of geometrically similar

bodies with the anterior body in a 𝑍

𝐷 = 2 orientation and a store separation displacement of

𝑥

𝑑 = 5 inches. In this

orientation the store feels significantly less drag at higher Reynolds number flows in both the y and z planes, so its

practicality is suited for modern applications.

7


IV. Conclusion

Interference drag is generated when two or more bodies experience high-velocity flow in tandem. The wake of the upstream body interferes with the posterior body resulting in a change in drag coefficient. While the non-axial forces applied to separated store are detrimental to its directional stability, the moments on the posterior store generated by the proximal upstream wake oscillations present the most danger to the store release carriage. This experiment did not measure supersonic flow interference drag, however any oblique shock interaction with previously aggravated boundary layers presents additional hazard to separated store orientation. The moment effects are caused by boundary layer separation due to the high-velocity flow between the separated store and the carriage. The increasingly turbulent nature of the boundary layer causes a gradient of shear stress across the surface of the store. This large, new frictional force applied non-uniformly on the missiles causes an unexpected torque on the system, effectively counteracting any store trajectory development. The separated stores become oriented against the flow, their resultant pressure vectors point back toward the carriage, and the two collide.

8


V. List of Figures

Figure 2: The test setup and the coordinate

Figure 3: Close up of ATI NANO25 sensor

Figure 4: Lateral Drag Coefficients, Z/D=1

Figure 5: Lateral Moment Coefficients, Z/D = 1

Figure 6: Lateral Drag Coefficients, Z/D = 2 Figure 7: Lateral Drag Coefficients, Z/D = 3

9



Figure 10: Vertical Drag Coefficients, Z/D = 1


Figure 11: Vertical Drag Coefficients, Z/D = 2

Figure 12: Vertical Drag Coefficients, Z/D = 3 Figure 13: Vertical Moment Coefficients, Z/D = 1

10


.

Figure 18: Axial Drag Coefficients, Z/D = 3

Figure 20: Axial Moment Coefficients, Z/D = 2

Figure 14: Vertical Moment Coefficients, Z/D = 2 Figure 15: Vertical Moment Coefficients, Z/D = 3

Figure 16: Axial Drag Coefficients, Z/D=1 Figure 17: Axial Drag Coefficients, Z/D = 2



Documents

AIAA Student Competition 2015 Research Paper