C162 Flight Mechanics: Project October 24, 2023
(Deadline: 6:00pm, November 21, 2023) !!! No late submissions !!!
Calculation of V1 (rejected takeoff speed) for an Airbus A380 taking off from SFO
!!! GOOD LUCK !!!
Goal of the project:
Calculate the maximum rejected takeoff speed (also known as V1) and the corresponding position the farthest along the runway from where an Airbus A380 with maximum takeoff weight can still safely come to a full standstill before it runs over the end of runway 28R at San Francisco International Airport.
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Given information: Airport information:

Length of runway 28R at SFO: S28R = 3,618 m

Elevation of the airport: sea level

Normal coefficient of rolling friction: r = 0.02

Coefficient of rolling friction while braking: r = 0.067
Height of wingtip above the ground: hwingtip = 7.8 m

Wingspan: b = 79.75 m

Total wing surface area: S = 845 m2

Span efficiency coefficient: e1 = 0.9
Aircraft aerodynamic properties:

Maximum lift coefficient in takeoff configuration: CL,TO = 1.423

Maximum lift coefficient in landing configuration: CL,L = 1.203

Parasitic drag coefficient at takeoff: CD,0 TO = 0.013

Parasitic drag coefficient with spoilers deployed: CD,0 spoilers = 1.1 CD,0 TO
Procedure:

Calculate the increasing speed profile along the length of the runway until takeoff.

Calculate the decreasing maximum speed profile along the length of the runway for
which the remaining runway length is sufficient to slow down to a full standstill.

Find the intersection between both curves, which gives you the position and the V1 speed
Some hints:

a) The main crux to find the aforementioned speed profiles along the runway length is using the equations that link velocity with distance. Note that we cannot assume a constant force acting on the object because the average speed is unknown here. See also e)

b) You don’t need to use the 20% and 30% values above stall speed Vstall for calculating VTO and VL, since the corresponding lift and parasitic drag coefficients for both are given.

c) You don’t need to use the 70% VTO or VL rule of thumb for calculating the average velocity during the entire maneuver (for calculating the average lift and drag forces), since we are calculating the actual lift and drag force at each time instant. See also e)

d) Please pay close attention that you define all the different forces in the correct direction (i.e., watch the signs of the forces in the equations!)
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e) Calculate the speed and distance by means of a loop, based on the following concepts for takeoff and landing, where you incrementally integrate acceleration towards speed and position over small time steps, until you reach the end of the runway:
s(t=0) = 0
v(t=0) = 0
a(t=0) = Feff(v(t=0))/m
s(t=tend) = l28R
v(t=tend) = 0
a(t=tend) = Feff(v(t=tend))/m
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Some checks to verify your results:

As a test to verify your procedure: the published takeoff distance of the A380 at MTOW is around: STO 2,900 m

Another test to verify your procedure: the published landing distance of the A380 at zero fuel weight is around: SL 2,150 m with Wzerofuel = 321,000 kg g0

The general shape of both curves should approximately look as follows:
Solution!
What you have to hand in:
You DON’T need to write a full report! We just need the following:

A solution document with the procedure that you followed to get the result and your boxed final answer. Please don’t forget units!

An executable Matlab mfile that calculates the velocity profiles and plots a figure, similar to the one above, but with tick labels.
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