A one-tenth-scale smaller model of a supersonic wing is tested at 700m/s in air

Question

A one-tenth-scale smaller model of a supersonic wing is tested at 700m/s in air at sea level, with rho = 1.225kg/m^3 and speed of sound a = 343m/s. The drag force of the model, D_M, is measured as 100N. What is the Mach number for the model? If the full-scale wing prototype flies at the same Mach number at 8km standard altitude, with rho = 0.525kg/m^3 and a = 308m/.s, what is the estimated prototype speed V_p? Assume that the Reynolds effects can be ignored, i.e., the drag coefficient C_D depends on Mach number only. Estimate the drag of the prototype flying at the same Mach number. Here, C_D = D/rho V^2 A, where D is the drag force, V is the flight speed, A is a certain reference area.

Explanation / Answer

(a)a=speed of sound

mach number=v/a=2.04

(b)Since mach number is same

2.04=V/308

V=628.32 m/s

(c)since Cd depends on mach number only

D/(rho*V^2*A) =constant

100/(1.225*700^2*Am)=D/(0.525*628.32^2*100Am)

we get D=3452.93

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