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Answer aircraft performance doc with answers from mod 3 and 4 doc.


1

 


 

Exercise 5: Aircraft Performance

 

For this week?s assignment you will revisit your data from previous exercises, therefore

 

please make sure to review your results from the last modules and any feedback that

 

you may have received on your work, in order to prevent continuing with faulty data.

 

1. Selected Aircraft (from module 3 & 4):

 

2. Aircraft Maximum Gross Weight [lbs] (from module 3 & 4):

 

2000 lbs.

 

Jet Performance

 

In this first part we will utilize the drag table that you prepared in module 4.

 

Notice that the total drag column, if plotted against the associated speeds, will give you a drag

 

curve in quite similar way to the example curves (e.g. Fig 5.15) in the textbook. (Please go

 

ahead and draw/sketch your curve in a coordinate system or use the Excel diagram functions

 

to depict your curve, if so desired for your own visualization and/or understanding of your

 

further work.)

 

Notice also that this total drag curve directly depicts the thrust required when it comes

 

to performance considerations; i.e. as discussed on pp. 81 through 83, in equilibrium flight,

 

thrust has to equal drag, and therefore, the thrust required at any given speed is equal to the

 

total drag of the airplane at that speed.

 

Last but not least, notice also that, so far, in our analysis and derivation of the drag table in

 

module 4, we haven?t at all considered what type of powerplant will be driving our aircraft. For

 

all practical purposes, we could use any propulsion system we wanted and still would come up

 

with the same fundamental drag curve, because it is only based on the design and shape of the

 

aircraft wings.

 

Therefore, let?s assume that we were to power our previously modeled aircraft with a jet

 

engine.

 

A. What thrust [lbs] would this engine have to develop in order to reach 260kts in level flight at

 

sea level standard conditions? Notice again that in equilibrium flight (i.e. straight and level, unaccelerated) thrust has to be equal to total drag, so look for the total drag at 260kts in your

 

module 4 table. (In essence, this example is a reverse of the maximum speed question ?

 

expressing it graphically within the diagram: We know the speed on the X-axis and have the

 

thrust required curve; that gives us the intercept point on the curve through which the

 

horizontal/constant thrust available line must go.)

 

B. Given the available engine thrust from A. above, what is the Climb Angle [deg] at 200kts and

 

Maximum Gross Weight? (Notice that climb angle directly depends on the available excess

 

thrust, i.e. the difference between the available thrust in A. above and the required thrust from

 

your drag curve/table at 200kts. Then, use textbook Eq. 6.5b relationships to calculate climb

 

angle).

 


 

This document was developed for online learning in ASCI 309.

 

File name: Ex_5_Aircraft Performance

 

Updated: 07/19/2015

 


 

2

 

C. What is the Max Endurance Airspeed [kts] for your aircraft? Explain how you derived at your

 

answer.

 

Prop Performance

 

In this second part we will utilize the same aircraft frame (i,e, the same drag

 

table/graph), but this time we will fit it (more appropriately and closer to its real world

 

origins) with a reciprocating engine and propeller.

 

D. To your existing drag table, add an additional column (Note: only the speed column, the total

 

drag column and this third new column will be required ? see below). To calculate the Power

 

Required in the new column, use textbook p. 115 equation and the V and D values that you

 

already have: Pr = D*Vk / 325

 

V

 

(KTAS)

 

VS

 

80

 

100

 

120

 

140

 

160

 

180

 

190

 

200

 

220

 

240

 

260

 


 

DT = Tr

 

(lb)

 


 

Pr

 

(HP)

 


 

Pr

 


 

maxE

 


 

maxR

 


 

V

 


 

E. Draw/sketch (or plot in an Excel diagram) your Power Required curve against the speed

 

scale from the table data in A. above. (Note: This step is again solely for your visualization and

 

to give you the chance to graphically solve the next questions in analogy to the textbook and

 

examples. See sketch above.)

 

F. Find the Max Range Airspeed [kts] for your aircraft. Remember from the textbook discussion

 

pp. 125 through 127 that Maximum Range Airspeed for a reciprocating/propeller driven aircraft

 

occurs where a line through the origin is tangent to the power required curve (see textbook Fig.

 

8.9 and sketch above). However, as per the textbook discussion, it is also the (L/D) max point,

 

which we know from our previous work on drag happens where total drag is at a minimum

 

(therefore, you can also reference the total drag column in your table and find the airspeed

 

associated with the minimum total drag value).

 

G. Find the Max Endurance Airspeed [kts] in a similar fashion. (Tip: The minimum point in the

 

curve will also be visible as minimum value in the P r column of your table.)

 

H. Let?s assume that the aircraft weight is reduced by 10% due to fuel burn (i.e. similar to the

 

gross weight reduction in Exercise 4, problem B).

 

This document was developed for online learning in ASCI 309.

 

File name: Ex_5_Aircraft Performance

 

Updated: 07/19/2015

 


 

3

 


 

I) Aircraft Weight [lbs] for 90% of Maximum Gross Weight (i.e. the 10% reduced weight

 

from above). Simply apply the factor 0.9 to your aircraft Maximum Gross Weight from

 

number 2. above:

 


 

your

 


 

II) Find the new Max Range Airspeed [kts] for the reduced weight. Remember (from

 

textbook reading and Exercise 4, B.) that the weight change influence on speed was

 

expressed by Eq. 4.2 in the textbook.

 


 

Landing Performance

 

For this last part of this week?s assignment you will continue with your reciprocating

 

engine (i.e. prop) powered aircraft and its reduced weight. Let?s first collect some of the

 

data that we already know:

 

3. Stall Speed for 90% of Maximum Gross Weight (i.e. the stall speed for 10% decreased

 

weight from above, which we already calculated in Exercise 4, problem B.):

 

I. Find the Approach Speed [kts] for your 90% max gross weight aircraft trying to land at a

 

standard sea level airport. Approach speed is usually some safety margin above stall speed

 

-.let?s assume for our case a factor of 1.2, i.e. multiply your stall speed from number 3. with a

 

factor of 1.2 to find the approach speed:

 

J. Determine the drag [lbs] on the aircraft during landing roll.

 

I) For simplification, start by using the total drag value [lbs] for stall speed (for the full

 

weight aircraft) from your module 4 table:

 


 

the

 


 

II) Adjust the total drag (from I) above) for the new weight (from H. I) above) by using

 

textbook Equation 7.1 relationship: D2/D1 = W2/W1

 


 

the

 


 

III) Find the average drag [lbs] on the aircraft during landing roll. A commonly used

 

simplification for the dynamics at play is to use 70% of the total drag at touchdown as

 

average value. Therefore, find 70% of your II) result above.

 


 

K. Find the frictional forces during landing roll. The Total Friction is comprised of Braking Friction

 

at the main wheels and Rolling Friction at the nose/tail wheel. For this example, let?s assume

 

that, in average, there is 75% of aircraft weight on the main wheels and 25% on the nose/tail

 

wheel over the course of the landing roll. The Average Friction Force is then the product of

 

respective friction coefficient and effective weight at the wheel/wheels (see p. 209 textbook):

 

F = *N

 


 

This document was developed for online learning in ASCI 309.

 

File name: Ex_5_Aircraft Performance

 

Updated: 07/19/2015

 


 

4

 

I) If the rolling friction coefficient is 0.02, what is the Rolling Friction [lbs] on the nose/tail

 

wheel? (Remember that only 25% of total weight are on that wheel and that the weight

 

was reduced by 10% from maximum gross weight ? see H I)):

 

II) If the main wheel brakes are applied for an optimum 10% wheel slippage (as

 

discussed on textbook pp. 209/210), what is the Braking Friction [lbs] on the main

 

wheels during landing roll on a dry concrete runway? Use textbook figure 13.9 to

 

determine the friction coefficient. (Remember that the weight on the main wheels is only

 

75% of total aircraft weight).

 

III) Find the total Average Friction [lbs] during landing by building the sum of I) and II):

 

L. Find the Average Deceleration [ft/s 2] during landing roll. Use the same rectilinear

 

relationships as in module 1, applying the decelerating forces of friction and drag from J. III) &

 

K. III) above. Assume that residual thrust is zero. (Keep again in mind that for application of

 

Newton?s second law, mass is not the same as weight. Your result should be a negative

 

acceleration value since the aircraft decelerates in this case.):

 

M. Find the Landing Distance [ft] (Remember that we start from a V0 at approach speed and

 

want to slow the aircraft to a complete stop, applying the negative acceleration that we found in

 

L. Also, remember to convert approach speed from I. above into a consistent unit of ft/s.):

 

N. If your aircraft was to land at a higher than sea level airport (e.g. at Aspen, Co) what factors

 

would change and how would it affect your previous calculations, especially your landing

 

distance. Explain principles and relationships at work and support your answer with applicable

 

formula/equations from the textbook. You can include example calculations to support your

 

answer:

 


 

This document was developed for online learning in ASCI 309.

 

File name: Ex_5_Aircraft Performance

 

Updated: 07/19/2015

 


 

 


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