Text Lecture 4e - Flight evenlope and instruments

Last time we treated the operational limits of an aircraft, which should never be exceeded.

The performance limits of an aircraft, describing what it is able to do may lie within the boundaries specified by the operational limits or they may exceed these limits. As you see in the figure, these limits are altitude dependent.

That seems difficult for a pilot.

How should he or she deal with monitoring these limits quickly when also piloting the aircraft?

Today I would like to address this issue by having a closer look at the indicators available to the pilot in the cockpit.

Let’s start with the stall speed of the aircraft.

As you can see, it increases with . Furthermore, this limit is dependent on the aircraft’s weight.

In equilibrium lift should equal weight and from that we can derive the equation for the minimum airspeed. A larger weight results in a higher stall speed.

So the worst case stall speed occurs at maximum aircraft weight. In order to monitor the speed, the pilot has an , which is part of the basic six instruments, always available in a cockpit.

The airspeed indicator is a pneumatic instrument, which means it is connected to two inputs, a pitot tube and a static port.

The pitot tube is measures the total air pressure and the static port measures the static pressure.

These two ports are carefully positioned on the airframe in order to provide the correct measurement.

Schematically, an airspeed indicator looks like this on the inside.

There is a sealed chamber which is connected to the static pressure port.

The total pressure is connected to a capsule which expands as a function of the internal pressure, the total pressure, and the external pressure, the static pressure.

The pressure difference is a measure for the airspeed and is provided to the dial through a set of gears.

For low speed applications, we can use Bernoulli’s law to determine the airspeed based on the pressure difference. The left hand side of the equation is the measured pressure difference. The right hand side is the dynamic pressure. However, we have a problem here. There is 1 equation with two unknowns!

The air density is unknown to the instrument and the airspeed as well.

So this cannot be solved.

A simple solution is to make an assumption for one of the variables. And that is exactly what is done.

It is assumed that the aircraft is flying at sea level conditions and thus, air density equals 1.225 kg/m3. Of course, this solves the problem of calculating a value but it also means that the airspeed provided by the indicator is incorrect!

It is not the but the equivalent airspeed.

It is equivalent to what it would be at sea level conditions.

So let’s write down the dynamic pressure. The airspeed in this equation is the true airspeed.

If we set air density equal to sea level conditions then airspeed becomes equivalent airspeed. If this is rewritten, then Ve equals the true airspeed multiplied with the square root of the ratio of the actual air density and the sea level air density. So the airspeed indicator is wrong, but what does this mean for our limit, the minimum airspeed? The minimum airspeed equation gives the minimum TRUE airspeed.

If we rewrite this to equivalent airspeed, then we obtain the following.

Vemin is a function of the sea level air density!

So minimum equivalent airspeed is independent of altitude.

This means that a limit on the dial always gives the correct stall speed, even though the absolute value in terms of true airspeed is incorrect!

On such a dial, the limit, indicated by the lower bound of the green bar, is always indicated for the worst case condition, maximum aircraft weight.

So if the pilot stays above this limit, he or she will always be clear of the stall speed!

That is nice isn’t it! In practice, the equations become a bit more complex if we include compressibility effects due to the .

However, the basic principle is the same. This may seem strange, an airspeed indicator that does not provide the right value but that is always correct when predicting the stall speed.

So how do we explain this from a physical point of view?

In essence, the airspeed instrument measures the dynamic pressure, and this is exactly what the wing experiences in the flow.

That is why it correctly predicts the stall condition. If we go back to the diagram with our limits, we can see that the maximum operating airspeed has the same shape as the stall speed.

This limit is also constant when expressed as equivalent airspeed.

On the airspeed indicator, this limit is indicated by the yellow bar. Flying above that speed is only safe in good atmospheric conditions without gusts.

So, two limits can be indicated with a fixed boundary on the airspeed indicator.

The maximum altitude indicated in the flight envelope can also easily be determined.

It works as follows.

The altimeter is one of the six basic instruments, connected to the static port.

On the inside of this instrument, there is a membrane which will expand to a certain level based on the static pressure inside the box.

The expansion of the membrane is a measure of the altitude. Unfortunately, the static pressure on sea level may vary, depending on the weather conditions. So again, this instrument may give incorrect readings if the pilot is interested in the distance to the ground.

Nevertheless, the maximum altitude in our flight envelope depends only on the static pressure outside the aircraft.

So the maximum altitude is a fixed pressure altitude and will thus be constant on this instrument.

This leaves us with only one operational limit to discuss.

The maximum operating Mach number. Aircraft which are able to fly in the transonic speed regime always have a Mach meter on board. The limit indicated here is a fixed Mach number and therefore also a fixed limit on the Mach meter.

It is beyond the scope of this lecture to explain how this instrument works exactly.

What I can say for now is that the Mach number can be determined from the pressure ratio of the dynamic pressure and the static pressure. The dynamic pressure is measured by the airspeed indicator and the static pressure by the altimeter.

If I now go back to the operational limits and the performance limits, then there is only one limit covered by the indicators.

The maximum airspeed limit.

This limit cannot be exceeded and therefore does not have to be indicated.

It will be reached when maximum power is applied at a constant altitude.

This concludes the discussion on how the pilot can monitor the limits whilst flying.