cpb-us-west-2-juc1ugur1qwqqqo4.stackpathdns.com · Web viewTo determine power required, the equation P R = 1 2 ρs C D0 3 + W 2 0.5ρsπARe V -1 was used. ρ is the air density at

AAE 2200: Introduction to Aerospace Engineering

Take-Home Portion of Final Exam

FLIGHT PERFORMANCE ANALYSIS

OF THE VAN’S RV-10 AIRCRAFT

Tevon Martinez

Lab Section: Monday 11:30

Lab Instructor: Kayleigh Gordon

Professor: Dr. James Gregory

Due Date: 12/10/2016 5pm

Mechanical and Aerospace Engineering Department

The Ohio State University

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Table of ContentsPurpose ............................................................................................................................................ 4

Background ...................................................................................................................................... 4

Task I: Drag Polar ............................................................................................................................ 5

Theory: ......................................................................................................................................... 5

Results: ........................................................................................................................................ 5

Discussion: ................................................................................................................................... 7

Task II: Power Required .................................................................................................................. 7

Theory: ......................................................................................................................................... 7

Results: ........................................................................................................................................ 8

Discussion: ................................................................................................................................... 8

Task III: Power Available ................................................................................................................ 9

Theory: ......................................................................................................................................... 9

Results: ........................................................................................................................................ 9

Discussion: ................................................................................................................................. 10

Task IV: Climb Performance ......................................................................................................... 11

Theory: ....................................................................................................................................... 11

Results: ...................................................................................................................................... 11

Discussion: ................................................................................................................................. 13

Task V: Range and Endurance ...................................................................................................... 14

Theory: ....................................................................................................................................... 14

Results: ...................................................................................................................................... 14

Discussion: ................................................................................................................................. 14

Task VI: Gliding Flight ................................................................................................................. 15

Theory: ....................................................................................................................................... 15

Results: ...................................................................................................................................... 15

Discussion: ................................................................................................................................. 16

Task VII: Turning Flight ............................................................................................................... 16

Theory: ....................................................................................................................................... 16

Results: ...................................................................................................................................... 17

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Discussion: ................................................................................................................................. 18

Task VIII: Takeoff and Landing Performance .............................................................................. 18

Theory: ....................................................................................................................................... 18

Results: ...................................................................................................................................... 19

Discussion: ................................................................................................................................. 19

Conclusions .................................................................................................................................... 19

References ...................................................................................................................................... 20

Appendix ........................................................................................................................................ 20

List of FiguresFigure 1: Drag Polar Curve .............................................................................................................. 6 Figure 2: Maximum Lift to Drag Curve .......................................................................................... 7 Figure 3: Power Required Curve ..................................................................................................... 8 Figure 4: Power Required vs. Power Available ............................................................................. 10 Figure 5: Rate of climb graph for three altitudes ........................................................................... 11 Figure 6: Maximum Rate of climb Curve ...................................................................................... 12 Figure 7: Climb Hodograph at Sea Level ...................................................................................... 13 Figure 8: Glide Hodograph at 10000 ft .......................................................................................... 16 Figure 9: V-n Diagram ................................................................................................................... 17 Figure 10: Vans RV-10 Three view diagram ................................................................................ 20

List of Tables Table 1: Task III Power Required/Power Available parameters ................................................... 10 Table 2: Best Climb Conditions .................................................................................................... 13

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PurposeThis purpose of this report is to provide an analysis of the Vans RV-10 aircraft. This is of importance to pilot’s and anyone interested in the purchase of the aircraft. This type of analysis provides value insight into values such as the stall speed of the aircraft, maximum speed, takeoff distance, landing distance, rate of climb, glide distance, range, endurance, and turn performance. Each of these metrics is important to safely fly the aircraft, efficiently fly the aircraft. This information is also necessary for figuring out flight plans for the aircraft.

Background

The Vans RV-10 is a 4-seat general aviation aircraft with a low wing. The vehicle has a maximum takeoff weight of W=2700 lbs. This weight is important to know for determining the lift that the aircraft can produce. The RV-10 has a wing area of 148 ft2, and wing span of 31.75 ft. These values are very important in determining the lift that the aircraft can produce. Parasitic drag coefficient after being calculated is CD0 = 0.0265, span efficiency as the Oswald efficiency factor “e” is found to be 0.8. The max coefficient of lift is given as CLmax = 1.77. The given max power at sea level, 5,000 ft and 10,000 ft respectively is 230 hp, 195 hp, and 165 hp. The specific fuel consumption at cruise speeds is 0.46 (lb/hr)/shp, and the cruise power is 165 hp. The usable fuel volume was given as 60 gallons of fuel. The density of the 100LL fuel which is used by the RV-10 is 6 lbs/gal. The propeller efficiency factor η is given as a function of freestream velocity. In task I, the calculation of drag polar, the relevant given factors were the parasitic drag coefficient, the maximum coefficient of lift and the Oswald efficiency factor, along with the aspect ratio, wing area, and wing span. In task II the necessary information for calculation of power required is the weight of the aircraft, the aspect ratio, the Oswald efficiency factor, wing area and any other variables necessary for the calculation of lift. In task III, the calculation of power available, the only necessary given information was the propeller efficiency in terms of the velocity in knots and the maximum power at each given altitude. This propeller efficiency allows for the calculation of power available at various airspeeds that the aircraft is travelling at. For task IV, calculation of the rate of climb, the necessary given information is the weight of the aircraft, the other necessary information was calculated in previous tasks. For task V, range and endurance are calculated utilizing the given specific fuel consumption, a constant propeller efficiency of η = 0.9, fuel volume, fuel density and the shaft horsepower of the engine. In gliding flight, task VI, weight was utilized to determine the velocity that must be flown at in order to fly for a maximum range at gliding flight. Gliding flight is flight at which the engine has no power. In calculating values for the turning flight in task VII, the given values for maximum positive load factor nmax=3.8 and negative maximum load factor nmin= -1.52, along with weight of the vehicle, and wing area were utilized to determine the conditions at which the aircraft performs

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turns optimally. For task VIII, the takeoff and landing distances were calculated using wing span values, gravitational constant, aspect ratio, Oswald efficiency factor, parasitic drag coefficient and mu, the value for coefficient of drag of the wheels of the aircraft at which rubber is in contact with a concrete runway. Mu for takeoff is given to be a unitless factor of 0.02, and at landing a factor of 0.05. In task VIII the maximum takeoff weight was utilized along with a given weight of 2400 lbs.

Task I: Drag Pola r

Theory: For calculation of the drag polar the equation CD=CD0+

CL2

πARe was utilized. CD0 and e had to be

estimated using the aerodynamic cleanliness method and the component build-up method to compute an average CD0 value. To use the aerodynamic cleanliness method a CF value was estimated from historical data, the wing area and wetted area had to be estimated from a given three view drawing, referenced below in the appendix as figure 9. CD0 was then calculated using

the equation CD0=fs=

CFSwet

s . In the utilization of the component build-up method, the drag for

each major component of the aircraft was estimated and then added up to find the total drag of the aircraft. After finding the component drag, an extra 25% drag was added on to the total to estimate for the drag of the landing gear. The same thing was done for the interference drag of the aircraft except by adding 10% to the total drag. In the estimation of e, the Oswald efficiency

factor, the equation e=1

k ' ' πAR+1+δ was used. K’’ was found from historical data along with δ .

AR, the aspect ratio of the wing was given as 6.81. The values of CLin the drag polar equation used in these calculations were the values from 0 to the given coefficient to lift max of 1.77. After estimation of parasitic drag and Oswald efficiency factor was done, a class average was given for calculation purposes. The given value of CD0 is 0.0265, the Oswald efficiency factor is given as e = 0.8. The L/D ratio was found simply by dividing CL/CD. This data was used to determine the maximum L/D ratio.

Results: First, the value for the wetted area of the plane was calculated to be 684 ft2 from the three view drawings. Using the CD0 equation, parasitic drag was calculated to be 0.0299. CF was found to be 0.0065 for this equation. Under the use of the component build-up method, the parasitic drag was calculated to be 0.0287. The average found for these values was CD0=0.0293. The Oswald efficiency factor was estimated to be 0.778. Using the given values of e and CD0, the drag polar calculated is shown below in figure 1. CD0 on this figure is the smallest distance to the x axis from the curve

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8C

L

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

CD

Graph of CD in terms of CL

Drag PolarCD0

Figure 1 : Drag Polar Curve

The plot of L/D ratio vs coefficient of lift is given below. The maximum Lift to Drag ratio from this data was determined to be L/Dmax = 12.708. The maximum lift to drag ratio in this case will be at the peak of this graph in figure 2.

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8C

L (Unitless)

0

2

4

6

8

10

12

14

L/D

(Uni

tless

)

L/D vs CL

Figure 2: Maximum Lift to Drag Curve

Discussion: This data is found above is very important in the determination of all other data in this analysis. Without the maximum lift to drag ratio, the velocity to fly at most efficiently would not be known. Without drag polar the performance of the vehicle would not be able to be determined at all. Using the maximum lift to drag ratio will allow for the calculation of the parameters for an efficient flight and the maximum boundaries of the aircraft’s performance.

Task II: Power RequiredTheory:

To determine power required, the equation PR=(12

ρsCD0)3

+( W 2

0.5 ρsπARe )V −1 was used. ρ is the

air density at each altitude for which power required is calculated, s is the wing area, AR is aspect ratio of the wing, previously discussed, and e is the Oswald efficiency factor. CD0 was calculated in task 1 to be 0.0265. The power required at each altitude will be different due to using different air densities at each altitude. To find the stall speeds of the aircraft at various

altitudes the equation V Stall=√ 2WρsCLMAX

, this equation is based off of the fact that stall speed

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occurs at coefficient of lift max. Speed for minimum power required was found using the Matlab program to find on the power required curve the minimum point along with the corresponding velocity at each altitude. The same thing was done for the speed for maximum lift-to-drag ratio.

Results: The power required calculated for sea level, 5000 ft and 10000 ft is shown below. At higher velocities the power required is lower higher in the atmosphere, while at low velocities the power required is lower at lower altitudes.

40 60 80 100 120 140 160 180Velocity(knots)

50

100

150

200

250

300

Pow

er R

equi

red

(HP

)

Power Required at various altitudes

Sea Level5000 ft10,000 ftStall SpeedsSpeed for min PrSpeed for max L/D

Figure 3: Power Required Curve

The velocities for stall speeds for sea level, 5,000 ft and 10,000 ft are 55.1760 knots, 59.4387 knots, and 64.2012 knots, respectively. The stall speed increases as altitude is increased. The speed for minimum power required for sea level, 5,000 ft and 10,000 ft are 68 knots, 73.2 knots, and 79.1 knots respectively. The speed for maximum lift to drag ratio for sea level, 5,000 ft and 10,000 ft are 89.413 knots, 96.32 knots, and 104.04 knots respectively. For each of these parameters the speed increases according to altitude.

Discussion: This data is very important to the pilot flying this aircraft. The pilot should know what his minimum speed before stalling is at various altitudes. If the pilot is unaware of this information, a crash is possible to occur if the pilot is unable to recover from a stall. The pilot should also be

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aware of the velocity to travel at for maximum lift to drag ratio in order to fly the aircraft most efficiently.

Task III: Power Available Theory: The power available is only dependent on the engine in the aircraft and the efficiency of the

aircraft at varying velocities. This propeller efficiency is denoted as η = 0.90(1−( 35V ∞ )

2

). The

efficiency factor is then multiplied by the maximum power available at each altitude. Using this new power available curve, the minimum speed and maximum speeds are then found graphically by finding the intersection points of power available and power required. However, for minimum speed, the velocity will be assumed to be stall speed because that speed is higher than the graphically found values.

Results: The figure below displays the results for the power required and power available curves. The top of the curves for each altitude represents the power available for each altitude. This curve logarithmically approaches the maximum horsepower at each altitude. For example, the maximum horsepower at that altitude is 230 horsepower. The vehicle will never be 100% efficient with a propeller, thus the curve will never reach that power.

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40 60 80 100 120 140 160 180Velocity(knots)

0

50

100

150

200

250

300

Pow

er(h

p)

Power Required vs Power Available Curve

Sea Level5000 ft10,000 ftStall SpeedsSpeed for min PrSpeed for max L/D

Figure 4: Power Required vs. Power Available

The data below represents the necessary information for the pilot to have at minimum speed the aircraft can travel at, AKA the stall speed in this case, the speed the pilot must travel for the max lift to drag ratio and the maximum speed where power available is equal to power required.

Table 1: Task III Power Required/Power Available parameters

Minimum Speed Speed for (L/D) max Maximum Speed

AltitudeV∞(knots)

PR(hp)

PA(hp) V∞(knots)

PR(hp)

PA(hp) V∞(knots)

PR(hp)

PA(hp)

Sea Level 55.18 54.11 123 89.4 58.3 175 165 198 1985,000 ft 59.4 58.3 115 96.3 62.8 152 162 167 16710,000 ft 64.2 62.3 105 104 67.83 131 158 141 141

Discussion: This information is crucial for the pilot to know. The pilot must know his absolute maximum speed he can travel at. As in task II this information is crucial for efficient and safe performance of the vehicle at various altitudes.

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Task IV: Climb Performance Theory: In climb performance the crucial factor to determine is maximum rate of climb, this was

determined through the use of the formula ROCmax= Pavailable−PrequiredW . In this case the

maximum power was used in order to get the maximum rate of climb. The maximum rate of climb was determined through Matlab by using the max function integrated into the vector of values determined for rate of climb across various velocities. After pulling the three maximum rate of climb values from sea level, 5000 ft and 10000 ft these values were graphed and determined to be linear. After forming a straight line of best fit to these values the absolute ceiling and service ceiling of rate of climb is equal to 100 ft/min could then be determined. In order to find the amount of time to climb to 10000 ft from sea level, the portion of the max rate of climb curve from sea level to 10000 ft was extracted and formed to an inverse rate of climb curve vector. The trapz Matlab function was then utilized to determine the integral of dh/droc. This value gives a time to climb from sea level to 10000 ft.

Results: The maximum rate of climb for sea level was determined to be 1430 ft/min, for 5000 ft max rate of climb was 1098 ft/min, for 10000 ft max rate of climb was 799 ft/minute. This data is the peak of each of the corresponding curves below.

40 60 80 100 120 140 160 180Velocity (knots)

-1000

-500

0

500

1000

1500

Rat

e of

Clim

b (ft

/min

)

Rate of Climb Graph

Sea Level5000 ft10000 ft

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Figure 5: Rate of climb graph for three altitudes

The Graph below is a plot of the best line of fit for the maximum rate of climb at sea level, 5000 ft and 10000 ft in the atmosphere. The absolute ceiling for the RV-10 based off the graph where rate of climb is equal to zero is 22,560 ft. The service ceiling for this vehicle is 20,970 ft. This is the point where the maximum rate of climb is equal to 100 ft/min on the graph. Based off of the results below, the time to climb from zero to 10000 ft was found to be 9.22 minutes at maximum rate of climb.

0 200 400 600 800 1000 1200 1400Rate of Climb (ft/min)

0

0.5

1

1.5

2

2.5

Alti

tude

(ft)

104 Max Rate of Climb at various altitudes

Figure 6: Maximum Rate of climb Curve

The graph below is the climb hodograph at sea level. This graph portrays how the horizontal and vertical speeds (rate of climb) are related to each other. The maximum rate of climb at sea level is the peak of this graph as that is the maximum vertical velocity of the vehicle. The table below has relevant information regarding the best rate of climb condition and the best climb angle condition.

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0 20 40 60 80 100 120 140 160 180 200Horizontal Velocity (knots)

0

2

4

6

8

10

12

14

16

18

20

Verti

cal V

eloc

ity (k

nots

)

Climb Hodograph at Sea Level

Figure 7: Climb Hodograph at Sea Level

The table below contains information regarding best rate of climb condition and best climb angle condition.

Table 2: Best Climb Conditions

Rate of climb(ft/min)

Climb angle(degrees)

Velocity(knots)

Best Rate of climb condition

1430 9.015 89

Best Climb angle condition

1258 10.34 68.1

Discussion: The climb performance information is relevant to the pilot to determine the best speed for maximizing rate of climb and at what angle the climb occurs. This information also allows the pilot to determine how quickly they can reach a target altitude and if they can clear terrain or obstacles in time to avoid crashes and potential danger. The pilot can also gather information that

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the aircraft has poorer climb performance at higher altitudes due to the air being thinner, thus generating less lift.

Task V: Range and Endurance Theory: Determining range and endurance of the aircraft at 10000 ft requires the Brequet range and endurance relations for a propeller aircraft. These equations are as follows

Range= ηsfc (C L

C D) ln (

W 0

W 1) Endurance= η

sfc (CL

32

CD)√2 ρs[W 1

−12 −W 0

−12 ]

W1 is the final weight of the aircraft after burning a specific amount of fuel, W0 is the initial weight of the aircraft. The initial weight is max weight at 2700 lbs. The final weight was the max weight minus the weight of fuel consumed, which was 90% of the fuel capacity in this case. The fuel used was 90% of the 60 gal tank, which in turn weighed 324 lbs in fuel. So the final weight of the vehicle after gliding is 2376 lbs. SFC is the specific fuel consumption of the aircraft described in the background of the report. η in this case is the propeller efficiency which is assumed to be constant in this case at an efficiency of 0.9. The coefficient of lift and drag are assumed to be constant at this point at well. Both of these values are the coefficient of lift and drag when the lift to drag ratio is maximized as this point is where the vehicle has the most efficient flight. In order to find the velocity at which the vehicle travels for maximum range the lift equation is rearranged to V=√2W / ρsCL. CL in this case is the coefficient of lift at max lift to drag. Weight is the initial weight and rho is the air density at 10000 ft. This velocity stays constant throughout the entire flight. The endurance of the vehicle is the maximum amount of time it can stay in the air.

Results: The range of the aircraft starting at 10000 ft was determined to be 1035.72 nautical miles. The endurance of the aircraft is 10:16:48 in decimal hours (hh:mm:ss). The velocity for these optimum conditions is 104 knots.

Discussion: This information is extremely relevant to the pilot to determine how far the aircraft can fly on the amount of fuel it has, how long it can idle at a specific altitude and the conditions that the vehicle must be flown at to maximize lift to drag, which is the conditions that the vehicle most efficiently performs these tasks.

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Task VI: Gliding Flight Theory:

Gliding flight is the conditions that the vehicle loses power and is flying on aerodynamic lift alone, no extra forces are acting on the vehicle. The glide angle at this point is calculated by

using θ=tan−1( 1

LD

max). Based off the freestream velocity and glide angle, the horizontal

velocity and vertical rate of climb can be determined using the equation V h=V ∞ cos (θ) and

V V=V ∞ sin (θ). The maximum range can then be determined by Range= H∗LD

max. The

velocity required for this maximum range to be acquired is obtained using the equation

Vmaxrange=√2W /scos (θ)ρCL

. Rho in this case is the air density at 10000 ft and theta is the

minimum theta found through the use of the Matlab function min. CL like always is the coefficient of lift at maximum lift to drag. The weight assumes is also maximum takeoff weight of the vehicle.

Results: The glide hodograph is displayed below. It is a function of vertical vs horizontal velocity at 10,000 ft. The maximum distance that the aircraft could reach an airfield at after losing power at 10,000 ft is 20.91 nautical miles. The velocity the pilot should try to fly at is 175 knots for the maximum range.

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0 50 100 150 200 250 300 350Horizontal Velocity

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Verti

cal V

eloc

ity

Glide Hodograph

Figure 8: Glide Hodograph at 10000 ft

The hodograph is a parabolic curve shaped like this because the vehicle is in free glide with no excess power. The vertical velocity is negative because the vehicle is heading down towards the earth, with a positive velocity being in an upwards direction.

Discussion: The pilot should be aware of this information in order to know the distance he could fly if he loses power at a given altitude. This could allow the pilot to safely know what airport they could reach, or determine the safest possible landing zone in the case of total loss of power.

Task VII: Turning Flight Theory: In turning flight, the vehicle has a restricted positive load limit factor of 3.8, the negative minimum load limit factor is -1.52. The aircraft should also never exceed 200 knots as to avoid structural damage due to high g’s. The variable n, or the load limit factor, is the L/W ratio. To

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determine the velocity of the maneuver point of the RV-10 the positive load limit factor is used in the equation V*¿√2nmaxW / ρCLs. After determining the turning point velocity, the load factor

for the velocities between 0 and V* knots is plotted using n=( 12ρV 2 sCL)/W . The turn radius

and the turn rate of the vehicle at the turning point were calculated using the following,

Radius= V 2

g √nmax2 −1

Turn Rate=g√nmax

2 −1V

Velocity in both of these case is the velocity of the turning point V*. G is the gravitational constant. The turn rate will be in radians/s and radius will be in ft.

Results:

The V-n diagram below is a graph of the Load factor (L/W) vs the velocity of the aircraft in knots. This graph is calculated at sea level. The top horizontal line represents the Positive limit load factor at which the vehicle should not exceed based off of limits set by the FAA. The bottom horizontal line represents the negative limit load factor. The dashed line represents the speed that the vehicle should never exceed at 200 knots.

0 20 40 60 80 100 120 140 160 180 200Velocity (knots)

-2

-1

0

1

2

3

4

Load

fact

or n

V-n Diagram

Maneuver Point

Figure 9: V-n Diagram

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The minimum turn radius of the RV-10 at standard sea level conditions and maximum takeoff weight is 279.4 ft. The max turn rate at these conditions is 0.650 radians/s.

Discussion: These parameters are important for the pilot to keep in mind while turning mainly because the stall speed will increase significantly as the turn angle is increased. The lift of the plane turns more and more horizontal meaning that less lift is being utilized to counteract the forces of gravity. The pilot has a good idea with these measurements the best turn he can make and the smallest turn he can make safely. The pilot has to be very careful not to push these limits as the aircraft can suddenly stall. Typically, on landing these boundaries can be pushed which can be especially dangerous as there is very little space to recover from a stall. The parameters defined by the FAA are also important to follow to avoid structural damage and avoid overloading the wings of the aircraft.

Task VIII: Takeoff and Landing Performance Theory: The Takeoff and landing performance of the vehicle takes into account the changing drag, and lift of the aircraft. As the takeoff is performed. The equation to calculate the takeoff ground roll

is SG=W V ¿

2

2 g Favg. Velocity of takeoff is calculated using the equation V ¿=1.2∗V stall. The

calculation of Favg is: Favg=T 0.707V ¿−1

2ρV 0.707V ¿

2 sCD−μ [W−12ρV 0.707V ¿

2 sCL]. The coefficient of

lift in this case is CL=1

2ϕπAReμ. Coefficient of drag is calculated by the drag polar equation

CD=CD0+ϕCL

2

πARe. To calculate ϕ for the RV-10 the equation ϕ=

( 16hb )

2

1+(16hb )

2 must be used. H for

the vans is the height of the above ground, which in this case is estimated to be 3 feet based off of the three view diagram provided. The constant μ is assumed to be 0.02 for takeoff flight based off of the principle of rubber wheels in contact with a concrete runway. This constant represents the rolling drag coefficient constant. μ for landing flight is 0.05. In landing flight, since the vehicle is decelerating the drag and rolling resistance will be functions of time and distance. The average force for landing flight is calculated using the equation

Favg=−12

ρV 0.707V TD

2 sCD−μ [W−12ρV 0.707V TD

2 sCL]. The touchdown velocity is equal to the 1.3

times the stall speed at that altitude. The coefficient of lift and drag are calculated the same way in takeoff as in touchdown so the equations will be the same as the equations above for CD, CL,

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and ϕ. The equation involved in calculating ground roll of landing for the aircraft is as follows:

SL=−W V TD

2

2g Favg.

Results: After using the above equations, the takeoff roll distance at sea level at maximum takeoff weight is estimated to be 1902.72 ft. The takeoff ground roll distance at 5000 ft and maximum takeoff weight is estimated to be 2208.1 ft. The takeoff ground roll distance at sea level and a takeoff weight of 2400 lbs is estimated to be 1691.31 ft. The touchdown rolling ground distance at sea level and maximum takeoff weight is estimated to be 3,791.6 ft. These values seem fairly large, so some conversions of units may be incorrect in this instance.

Discussion: The results above describe how much runway space the Vans RV-10 requires at various weights and altitudes to take off. As weight is increased the distance to takeoff increases. As altitude increases, the distance required to take off also increases. The pilot and airport must know this information to know if an aircraft can land and takeoff on a runway or not. If the runway is not as long as these values, then the aircraft cannot use the runway at all.

ConclusionsFlight performance analysis is important for all aspects of flight. Analysis of wing configuration, drag polar of the aircraft, aircraft weight and the propulsion system that powers the aircraft allows for the understanding of many aspects of flight. These include glide distance, parameters for most efficient flight, rate of climb and all the other aspects included in this report. Without this knowledge the pilot would be unaware of the capabilities of their aircraft. It is vital that the pilot knows how steep of a bank he can take on turns and how slow he can fly without crashing. The safety of all passengers depends on the correct performance analysis of the aircraft. The vehicle’s range, endurance, speed, and altitude throughout flight all are variable based off of this type of analysis.

An important concept I learned in this case was the very important concept of keeping track of units and staying organized. I had to make sure I made comments on my Matlab code in order to not be confused and get incorrect units in my final answers. The organization of variables and units in this project was vital for completing the project in a reasonable amount of time. Throughout the project I experienced frustrating hours where my unreasonable answers were solved by adding a conversion factor after breaking down an equation extremely carefully. This concept combined with the concept of planning ahead allowed for the success of this project to occur. This project took many hours to complete, which is why we had to start as soon as we were able to. I felt responsible trying to complete tasks the day that we learned concepts about them. An interesting concept learned about flight analysis was the principle of propeller

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efficiency. I had not realized that the vehicle’s peak power is a variable of airspeed, but after discussing the principle that the tips of the propeller create shocks at high speeds makes sense because the propeller tips approach Mach 1 as speed of the aircraft increases. The propeller tips are also spinning, so this occurs at a much lower speed than Mach 1 of the aircraft. I also thought the concept of turning flight was important as well. Most of our other analysis involves no lateral or horizontal rolling of the vehicle, instead the vehicle would be in steady level flight. This turning flight analysis I thought was very interesting to observe.

ReferencesNot Applicable

Appendix

Figure 10: Vans RV-10 Three view diagram

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MATLAB CODE

%Final Project Aerospaceclc, clear, close all s = 148; %ft^2 wing areab = 31.75; %ft spanAR = (b^2)/s; %Aspect ratioCD0 = 0.0265; %parasitic drag coefficiente = 0.8; %oswald efficiency factorCL = [0:0.001:1.77]; %All possible lift coefficient valuesfprintf('Calculated value of CD0 was 0.293, value for e was 0.778.\n') %%%Task 1CD = CD0 + CL.^2 ./ (e*3.1415*(b^2)/s); figure(1)plot(CL, CD, 0, CD0, 'd') %Drag Polar Curvetitle('Graph of C_D in terms of C_L')legend('Drag Polar', 'C_D_0')xlabel('C_L')ylabel('C_D') LD = CL./CD;figure(2)plot(CL, LD) %L/D vs CLtitle('L/D vs C_L')xlabel('C_L (Unitless)')ylabel('L/D (Unitless)')grid ongrid minor LDmax = max(LD);fprintf('The Max L/D ratio is %g\n', LDmax) %%%Task 2 - Power RequiredVknots = [40:0.1:180]; %Velocity in knotsV = Vknots * 1.68781; %Velocity in ft/sW = 2700; %Lbsrho1 = 0.0023769; %Sea level density in english unitsrho2 = 0.0020482; %Density at 5000 ftrho3 = 0.0017556; %Density at 10000 ft Pr1 = (0.5*rho1*s*CD0)*V.^3 + (W^2/(0.5*rho1*s*pi*AR*e))*V.^-1;

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Pr2 = (0.5*rho2*s*CD0)*V.^3 + (W^2/(0.5*rho2*s*pi*AR*e))*V.^-1;Pr3 = (0.5*rho3*s*CD0)*V.^3 + (W^2/(0.5*rho3*s*pi*AR*e))*V.^-1; Pr1hp = Pr1./550;Pr2hp = Pr2./550; %Convert to HorsepowerPr3hp = Pr3./550; %Finding V StallsVs1 = sqrt(2*W/(rho1*s*max(CL)));Vs2 = sqrt(2*W/(rho2*s*max(CL))); %Stall Speed in ft/sVs3 = sqrt(2*W/(rho3*s*max(CL))); Pr1vs = ((0.5*rho1*s*CD0)*Vs1^3 + (W^2/(0.5*rho1*s*pi*AR*e))*Vs1^-1)/550;Pr2vs = ((0.5*rho2*s*CD0)*Vs2^3 + (W^2/(0.5*rho2*s*pi*AR*e))*Vs2^-1)/550;Pr3vs = ((0.5*rho3*s*CD0)*Vs3^3 + (W^2/(0.5*rho3*s*pi*AR*e))*Vs3^-1)/550; Prvs = [Pr1vs, Pr2vs, Pr3vs];Vs = [Vs1, Vs2, Vs3]./1.68781; %Find Speed for minimum PrVminpr1 = Vknots(find(Pr1 == min(Pr1)));Vminpr2 = Vknots(find(Pr2 == min(Pr2)));Vminpr3 = Vknots(find(Pr3 == min(Pr3))); Prmin1 = min(Pr1)/550;Prmin2 = min(Pr2)/550; %Prmin in ftlb/sPrmin3 = min(Pr3)/550; Prmin = [Prmin1, Prmin2, Prmin3];Vminpr = [Vminpr1, Vminpr2, Vminpr3]; %Speed for maximum L/D ratioCLm = CL(find(LD == max(LD))); %Coefficient of lift at max L/D RatioCDm = CD(find(LD == max(LD)));Vm1 = sqrt(2*W/(rho1*s*CLm));Vm2 = sqrt(2*W/(rho2*s*CLm)); %Velocity in ft/sVm3 = sqrt(2*W/(rho3*s*CLm));Vm = [Vm1, Vm2, Vm3]./1.68781; PrLD1 = ((0.5*rho1*s*CD0)*Vm1^3 + (W^2/(0.5*rho1*s*pi*AR*e))*Vm1^-1)/550;PrLD2 = ((0.5*rho2*s*CD0)*Vm2^3 + (W^2/(0.5*rho2*s*pi*AR*e))*Vm2^-1)/550;

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PrLD3 = ((0.5*rho3*s*CD0)*Vm3^3 + (W^2/(0.5*rho3*s*pi*AR*e))*Vm3^-1)/550;PrLD = [PrLD1, PrLD2, PrLD3]; figure(3)plot(Vknots, Pr1hp, Vknots, Pr2hp, Vknots, Pr3hp, 'g');title('Power Required at various altitudes')xlabel('Velocity(knots)')ylabel('Power Required (HP)')grid ongrid minorhold onplot(Vs, Prvs, 'rd'); plot(Vminpr, Prmin, 's'); plot(Vm, PrLD, 'o')legend('Sea Level', '5000 ft', '10,000 ft', 'Stall Speeds', 'Speed for min Pr', 'Speed for max L/D')hold off %%%Task 3 - Power AvailableProp = 0.90*(1-(35./Vknots).^2); MaxP1 = 230; %Max power in knots (sea level)MaxP2 = 195; %5000 ftMaxP3 = 165; %10000 ft Pa1 = Prop*MaxP1;Pa2 = Prop*MaxP2; %Max Power in HPPa3 = Prop*MaxP3; hold onplot(Vknots, Pa1,'b', Vknots, Pa2, 'r', Vknots, Pa3, 'g');ylabel('Power(hp)')title('Power Required vs Power Available Curve')hold off %%%Task 4 - Rate of Climb %part a%Rate of climbs for each altituderoc1 = 60*(Pa1*550-Pr1)./W;roc2 = 60*(Pa2*550-Pr2)./W;roc3 = 60*(Pa3*550-Pr3)./W;

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figure(4)plot(Vknots, roc1, Vknots, roc2, Vknots, roc3)title('Rate of Climb Graph')xlabel('Velocity (knots)')ylabel('Rate of Climb (ft/min)')legend('Sea Level', '5000 ft', '10000 ft')vmaxclimb1 = Vknots(find(roc1 == max(roc1)));vmaxclimb2 = Vknots(find(roc2 == max(roc2)));vmaxclimb3 = Vknots(find(roc3 == max(roc3))); %Part bmroc1 = max(roc1);mroc2 = max(roc2); %Max rate of climbs in ft/minmroc3 = max(roc3);mroc = [mroc1, mroc2, mroc3];alt = [0, 5000, 10000]; figure(5)plot(mroc, alt, 'd')coeffs = polyfit(mroc, alt, 1);fittedX = linspace(0, mroc1, 300);fittedY = polyval(coeffs, fittedX);hold onplot(fittedX, fittedY, 'r-', 'linewidth', 1);axis([0, mroc1, 0, 25000])title('Max Rate of Climb at various altitudes')ylabel('Altitude (ft)')xlabel('Rate of Climb (ft/min)')grid minorgrid onhold off %Part ch = 0:0.1:10000;rocvector = linspace(mroc1, mroc3, length(h)); %ROC max for rocinv = 1./rocvector;timeclimb10000 = trapz(h, rocinv); %Time to climb in minutes figure(6)plot(h, rocinv)title('Plot to Determine Time to Climb')xlabel('Altitude (ft)')ylabel('1/Roc_m_a_x (1/ft/min)') fprintf('The amount of time to climb from Sea level to 10000 ft is %4.2f minutes\n',timeclimb10000);

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%Part dangle = asind((roc1/60)./V);anglemax = max(angle);vhor = (Vknots).*(cosd(angle));vhorm = vhor(find(angle == anglemax)); figure(9)plot(vhor, (roc1.*60)./6076.14)axis([0, 200, 0, 20])title('Climb Hodograph at Sea Level')xlabel('Horizontal Velocity (knots)')ylabel('Vertical Velocity (knots)') %%%Task 5 - Range & Endurancealt = 10000; %Altitude is at 10000SFC = 0.46; % (lb/hr)/shpSFCs = 0.46/3600/550; %INTO (lb/s)/shppropr = 0.9;fvol = 60; %60 Gal of fuel spacefw = (fvol*6)*0.9; %Pounds of fuel used after 90% consumptionshp = 165; %shaft horsepower at 10000 ft R = propr/SFCs * max(LD) * log(W/(W-fw)); %Range in feetRnautical = R/6076.12;fprintf('The max range in Nautical miles is %4.4f\n', Rnautical) %Find Velocity that is used for max rangeVmaxrange = sqrt(2*W/(rho3*s*CLm))/1.68781; %Velocity in knotsfprintf('The velocity for max range is %4.2f knots\n',Vmaxrange) E = propr/SFCs*(CLm^(3/2)/CDm)*sqrt(2*rho3*s)*((W-fw)^(-.5)-W^(-.5));E = E/3600;fprintf('The Endurance of the aircraft is %4.4f hours\n',E) %%%Task 6 - GLIDING FLIGHT theta = atand(1./(LD));freestreamV = sqrt((2*W/s*cosd(theta))./(rho2*CL));Vhorizontal = freestreamV.*cosd(theta)*(3600/6076.14);

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Vvertical = freestreamV.*sind(theta)*(3600/6076.14); figure(7)plot(Vhorizontal, -Vvertical)title('Glide Hodograph')xlabel('Horizontal Velocity')ylabel('Vertical Velocity')grid ongrid minor H = 10000; %Altitude of 10000 ft Rmax = H*(max(LD))/6076.14; %Range for gliding flight fprintf('The max range after losing power at 10000 ft is %4.4f nautical miles\n',Rmax) Vmaxrange = sqrt((2*W/s*cosd(min(theta)))./(rho3*CLm)); %Velocity for max range at 10,000 ft %%%Task 7 - Turning Flightnmax = 3.8;nmin = -1.52;Vmax = 200; %never exceed velocity in knotsVstar = sqrt(2*nmax*W/(rho1*CL(end)*s))/1.68781; Vn = [0:0.01:Vstar]; %Velocities that will be graphed between 0 and V* n = (0.5*rho1.*((Vn*1.68781).^2)*s*CL(end))./W; %Load Factor for velocities Vmin = sqrt(2*nmin*W/(rho1*-CL(end)*s))/1.68781;Vnmin = [0:0.01:Vmin];nbot = (0.5*rho1.*((Vnmin*1.68781).^2)*s*-CL(end))./W; %Positive limit load factor vpos = [Vstar:0.1:200];npos = nmax*(vpos./vpos);vneg = [Vmin:0.1:200];nneg = nmin*(vneg./vneg); VertLine = [200, 200];nverline = [nmax, nmin];

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figure(8)plot( Vstar, nmax, '*', Vn, n, 'b', Vnmin, nbot, 'b', vpos, npos, 'b', vneg, nneg, 'b', VertLine, nverline, 'b:')axis([0, 210, -2, 4])title('V-n Diagram')xlabel('Velocity (knots)')ylabel('Load factor n')legend('Maneuver Point')grid ongrid minor g = 32.17; %Grav constant TurnR = (Vstar*1.68781)^2/(g*sqrt(nmax^2 - 1));fprintf('The min turn radius is %4.3f ft\n', TurnR) TurnRate = g*sqrt(nmax^2 - 1)/(Vstar*1.68781);fprintf('The max turn rate is %4.3f rate\n',TurnRate) %Radians/Second %%%Task 8 - Takeoff and Landing Distance %Takeoff velocityVto1 = 1.2*Vs1;Vto2 = 1.2*Vs2;mu = 0.02;h = 3;phi = (16*h/b)^2/(1+(16*h/b)^2);g = 32.17; Cl = (0.5*phi)*pi*AR*e*mu;Cd = CD0 + (phi*Cl^2)/(pi*AR*e); %FavgPowerRequired = (0.5*rho1*s*CD0)*Vto1^3 + (W^2/(0.5*rho1*s*pi*AR*e))/Vto1;Favg1 = PowerRequired/(0.707*Vto1) - 0.5*rho1*((0.707*Vto1)^2)*s*(Cd) - mu*(W-0.5*rho1*((0.707*Vto1)^2)*s*Cl); SG1 = (W*Vto1^2)/(2*g*Favg1);fprintf('Takeoff ground roll distance (SL, Max weight): %4.2f ft\n',SG1) %Part b at 5000 ft with Max Weight

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PowerRequired = (0.5*rho2*s*CD0)*Vto2^3 + (W^2/(0.5*rho2*s*pi*AR*e))/Vto2;Favg2 = PowerRequired/(0.707*Vto2) - 0.5*rho2*((0.707*Vto2)^2)*s*(Cd) - mu*(W-0.5*rho2*((0.707*Vto2)^2)*s*Cl); SG2 = (W*Vto2^2)/(2*g*Favg2);fprintf('Takeoff ground roll distance (5000 ft, Max weight): %4.2f ft\n',SG2) %Part c at SL with 2400 lbs weightW2 = 2400;Vs1new = sqrt(2*W2/(rho1*s*max(CL)));Vto3 = Vs1new*1.2; PowerRequired = (0.5*rho1*s*CD0)*Vto3^3 + (W2^2/(0.5*rho1*s*pi*AR*e))/Vto3;Favg3 = PowerRequired/(0.707*Vto3) - 0.5*rho1*((0.707*Vto3)^2)*s*(Cd) - mu*(W2-0.5*rho1*((0.707*Vto3)^2)*s*Cl); SG3 = (W2*Vto3^2)/(2*g*Favg3);fprintf('Takeoff ground roll distance (SL, 2400 pounds): %4.2f ft\n',SG3) %Part d Landing at SL with max weight and standard sea levelmu = 0.05;Vtd = 1.3*Vs1; Favg4 = -0.5*rho1*(0.707*Vtd)^2*s*Cd - mu*(W - 0.5*rho1*(0.707*Vtd)^2*s*Cl); SL = -W/(2*g*Favg4)*(Vtd^2); fprintf('Landing Roll distance (SL, Max Weight): %4.2f ft\n',SL)

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