Vy is always greater than Vx. Why?

[joshuahsong]

Hi all.
Why Vy should always greater than Vx speed?
Could someone explain in terms of physics and aerodynamics?

[maximus610]

I think it can be either equal...

[keith williams]

VX
In a steady climb:

a. The thrust acts up the climb path.
b. The drag acts down the climb path.
c. So the resultant force acting up the flight path is thrust minus drag.
d. Weight acts vertically downwards.

If you sketch these forces you will find that the sine of the climb angle = (thrust – drag) / weight. This sketch can be found in most aerodynamic text books.

For all angles between zero an ninety degrees, increasing the sine of the angle increases the angle. So for any given weight, the climb angle is greatest when flying at the speed at which the (thrust – drag) is maximum. Thrust – drag is called the excess thrust. The speed at which excess thrust and climb angle are maximum is called Vx.

VY
When an aircraft climbs, mechanical work is done power in moving the aircraft vertically upwards against the opposing forces of weight plus the vertical component of drag. If we increase the rate of climb, we increase the rate at which this mechanical work must be done. Power is the rate of doing work, so the rate of climb is a maximum when flying at the speed at which the maximum amount of power is available to push the aircraft vertically upwards.

Some of the power available from the engines must be used to maintain the airspeed by pushing the aircraft forward against the drag force. This part of the power is called the power required. If the engines are able to produce any power in excess of this power required, then the excess power can be used to provide a rate of climb. For any given amount of excess power, the rate of climb will decrease with any increase in aircraft weight. This leads to the following equation:

Rate of climb = excess power / weight.

This means that for any given aircraft weight, the rate of climb is maximized when flying at the speed at which the excess power is maximum. This speed is called Vy.

VX AND VY
So Vx is the speed at which excess thrust is a maximum and Vy is the speed at which excess power is available. The location of Vx on the speed range can be estimated by comparing the thrust and drag curves found in any aerodynamics text book. The location of Vy can be estimated by comparing the power available and power required curves. For all aircraft types these comparisons will show that at normal operating altitudes the speed Vx is less than the speed Vy.

EFFECT OF INCREASING ALTITUDE
As altitude increases in a climb at any given CAS and weight, the drag remains approximately constant. But the reducing air density reduces the mass flow of air passing through the engines. This in turn reduces both the thrust and the power available. So the best angle of climb and the best rate of climb both gradually decrease as the altitude increases. If the aircraft continues to climb, it will eventually reach an altitude at which there is just sufficient thrust and just sufficient power available to maintain the airspeed. This altitude is called the Absolute Ceiling.

At the Absolute Ceiling there is no excess thrust and no excess power to enable the aircraft to climb, so the aircraft will be just able to maintain level flight. Because drag and power required vary with airspeed, there will be only a single speed at which sufficient thrust and power are available for level flight. This means that the values of VX and VY must converge to this single speed as altitude increases towards the absolute ceiling.

So at altitudes lower than the absolute ceiling Vx is always less than Vy. As altitude increases Vx and Vy converge until they become the single speed at which level flight is possible at the absolute ceiling.

[pineappledaz]

On an excess power vs TAS graph Vx is the tangent, Vy is the maximum. As said above, Vy is the maximum rate of doing work, which occurs at the peak of the excess power graph. Vx is the best ratio of Work/Distance

Flight Testing Formulae (http://www.zapper.orconhosting.net.nz/raafsims/aerodynamics.html) shows a basic graph