Question

what will happen to the speed of aircraft if the mass of the same reduces during the flight but the enginie force remains the same ??

Answer 1

What will happen to the speed of aircraft if the mass of the same reduces during the flight but the engine force remains the same?

Solution.

From the theory aerodynamics of the flight: an aircraft flies horizontally, when:

$$Y = m g;$$ $$X = F.$$

in these equations:

$Y$ - the force of the lift;

$mg$ - a weight of the aircraft;

$F$ - the force of the thrust;

$X$ - a force of the drag is opposed to the thrust.

$$Y = C _ {L} \frac {\rho v ^ {2}}{2} S;$$ $$X = C _ {D} \frac {\rho v ^ {2}}{2} S;$$

in these formulas:

$C_L$ - lift coefficient;

$C_D$ - drag coefficient;

$S$ - a wings area;

$v$ - a speed of the aircraft;

$\rho$ - a density of the air.

We have:

$$m _ {1} g = C _ {L} \frac {\rho_ {1} v _ {1} ^ {2}}{2} S;$$ $$F = C _ {D} \frac {\rho_ {1} v _ {1} ^ {2}}{2} S;$$

If the mass of the aircraft reduces $m_2 < m_1$ , then:

$m_{2}g < C_{L}\frac{\rho_{1}v_{1}^{2}}{2} S$ – an aircraft climbs up, where the density of the air is less $\rho_{2} < \rho_{1}$ (if altitude increases then the air density decreases) and $m_{2}g = C_{L}\frac{\rho_{2}v_{1}^{2}}{2} S$.

The engine force remains the same, but $\rho_{2} < \rho_{1}$, then the speed of aircraft increases $v_{2} > v_{1}$ until a force of the drag is equal the force of the thrust $F = C_{D} \frac{\rho_{2} v_{2}^{2}}{2} S$.

The altitude changes until:

$$m_{2}g = C_{L} \frac{\rho_{2} v_{2}^{2}}{2} S$$

and

$$F = C_{D} \frac{\rho_{2} v_{2}^{2}}{2} S.$$

Therefore, if the mass of the aircraft reduces during the flight but the engine force remains the same, the speed of the aircraft increases.

**Answer**: if the mass of the aircraft reduces during the flight but the engine force remains the same, the speed of the aircraft increases.