Istanbul Technical University Faculty of Aeronautics and Astronautics
2017-2018 Fall Semester
11729 DNK201E Dynamics
Quiz – 2 SOLUTION
Problem: A jet airplane with a mass of
has a touchdown speed of
, at which
instant the braking parachute is deployed and
the power shut off. If the total drag on the
aircraft varies with velocity as shown in the
accompanying graph, calculate the distance
along the runway and time required to reduce
the speed to
. Approximate the
variation of drag by an equation of the form
, where is a constant.
Solution:
Value of the constant
For
is found from the
graph:
:
Distance and time can be found exactly by integration as shown below:
Alternative solution:
23.10.2017
Although not asked series expansions and graphs of position, velocity and acceleration are given below:
x-t graph:
250
200
150
100
50
1
2
3
4
5
v-t graph:
100
80
60
40
20
0
0
1
2
3
4
5
1
2
3
4
5
a-t graph:
0
5
10
15
20
25
30