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




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




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





This document was developed for online learning in ASCI 309.


File name: Ex_5_Aircraft Performance


Updated: 07/19/2015





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




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































DT = Tr






















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






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:






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:






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






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





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





This document was developed for online learning in ASCI 309.


File name: Ex_5_Aircraft Performance


Updated: 07/19/2015




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Oct 15, 2019





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