Need help with this problem. Is the problem 2.5 from the book performance and st
ID: 1842568 • Letter: N
Question
Need help with this problem. Is the problem 2.5 from the book performance and stability of aircraft by J.B. Russell (Chapter 2).
An aircraft has the following characteristics as a function of Mach number at a certain
altitude:
The aircraft has a mass of 90 000 kg and the wing area is 200 m 2. Find the maximum
level flight Mach number if the atmospheric pressure at this altitude is 9.6 kN m -2. (A)
2.5 An aircraft has the following characteristics as a function of Mach number at a certain altitude: 1.9 Mach number 1.7 2.1 0.01 0.00775 0.00875 0.007 No-lift drag coefficient (Lift-dependent coeff.)/Ci 0.56 0.63 0.41 0.46 Thrust (kN) 116 128 131 126 The aircraft has a mass of 90 000 kg and the wing area is 200 m2. Find the maximum level flight Mach number if the atmospheric pressure at this altitude is9.6 kN m 2. (A)Explanation / Answer
In this problem,
atmospheric pressure is 9.6 kpa,
the corresponding properties at this pressure are
h = height = 16438.61 m
T = 216.650 K
Velocity of Sound = 295.070 m/s
density = 0.154365 kg/m3
from the table using trial and error method, verifying different Mach numbers for above mentioned properties,
after calculating different Mach number Mach number = 1.7 gives
Mach = 1.7
Velocity of aircraft = 501.619 m/s
Lift of aircraft = mg = 90000*9.81 = 882900 N
Let us verify the Drag for Mach = 1.7
Cd = Cdo + Cdi
= 0.01 + 0.03127
= 0.03127
D = (1/2)*(Cd)*(density)*(Area)*(Velocity)2
D = (0.5)*(0.03127)*(0.15436)*(200)*(251071.1449)
D = 122 KN
which is approximately matches with Mach= 1.7
if we further calculate valuea it decreases considerably
for level flight D = T,
it will be satisfied only by Mach = 1.7 and below