Question

Which of the following is the correct performance equation?

(a) \(\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2-\frac{V}{g}\big\}\)

(b) \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2-\frac{V}{g}\big\}\)

(c) \(\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2+\frac{V}{g}\big\}\)

(d) \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2+\frac{V}{g}\big\}\)

I had been asked this question in my homework.

My doubt stems from Aerodynamic Relationships topic in division Aircraft Force Systems and the Equations of Motion of Aircraft Performance

Answer 1

Correct option is (d) \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2+\frac{V}{g}\big\}\)

Easiest explanation: The correct equation is \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=Emax\(\big\{sin\gamma_2+\frac{V}{g}\big\}\) where λ is dimensionless power, u is relative speed, τ is dimensionless thrust, Emax is maximum efficiency, sinγ2 is horizontal component, V is airspeed and g is gravitational force.