Use of pitot static tube for calculation of airplane velocity

[srn]

Posted this in the coursework forum as well but it doesn't appear any aerospace engineer visits that one :-) I'm supposed to help someone with this for his essay but I don't completely understand it myself.

I understand how a pitot tube measures the total pressure, and how a static pressure orrifice measures the static pressure. Assuming incompressible flow Bernoulli's equation provides a relation between these two, e.g. the fluid velocity at the orrifice location's becomes v = sqrt ( 2 * (total pressure - static pressure) / rho ).

But how can you make the connection between the measurement of the fluid velocity at this point and it being the aircraft's true speed? The pressure varies constantly over and under the airfoil, which means the fluid velocity changes constantly as well. Which also means different placements of the static port would give different fluid velocities. How do you know even where to put this, in order to get the aircraft's V?

 

[Cyrus]

Posted this in the coursework forum as well but it doesn't appear any aerospace engineer visits that one :-) I'm supposed to help someone with this for his essay but I don't completely understand it myself.

I understand how a pitot tube measures the total pressure, and how a static pressure orrifice measures the static pressure. Assuming incompressible flow Bernoulli's equation provides a relation between these two, e.g. the fluid velocity at the orrifice location's becomes v = sqrt ( 2 * (total pressure - static pressure) / rho ).

But how can you make the connection between the measurement of the fluid velocity at this point and it being the aircraft's true speed? The pressure varies constantly over and under the airfoil, which means the fluid velocity changes constantly as well. Which also means different placements of the static port would give different fluid velocities. How do you know even where to put this, in order to get the aircraft's V?

This is a very good post, because it is a very keen observation you made. The answer is found by testing different locations on the aircraft and placing the port where it introduces the least amount of error. The error won't go away to zero; but, it is minimized at the 'best' location. The pilot is given reference tables to correct for this, called 'installation errors'. In fact, if the port becomes clogged there is an alternative port the pilot can use. The pilots handbook has corrections for this port as well. Typically, the backup port uses the aircrafts cabin pressure.

 

[srn]

That explains, thank you Cyrus!

There was another thing I was wondering, the different airspeeds. If I understand it correctly, IAS is what is displayed on the airspeed indicator in the cockpit (using v = sqrt ( 2 * (total pressure - static pressure) / rho ))), CAS is IAS corrected for positioning errors (like the one you just explained, I suppose).
Now, some sources say EAS is CAS corrected for compressibility. But another says that EAS is the speed at sealevel at which the dynamic pressure is the same as the dynamic pressure for TAS at the plane's altitude. How does a minor fix for compressibility suddenly becomes a replacement of all rho by rho(sea level) in all equations? Because that's essentialy what you do right, in the above Bernoulli equation rho gets replaced by the rho value at sea level?
Some other source said that EAS is used for lower budget aircraft that cannot measure rho and hence use rho(sea level), which makes more sense than "correct for compressibility".

Also, if these are simply calculations, I assume that modern aircraft then display CAS instead of IAS?

--

Oh, and what do you mean with "Typically, the backup port uses the aircrafts cabin pressure"? Does this mean the static port is on the inside, or that instead there is no port but a direct connection from the cockpit to the airspeed indicator that "feeds" the static pressure?

 

[pitts]

I would like to add the little bit of knowledge I have being a aircraft mechanic. Most pitot tubes are in one of three locations. The most common on the bottom of the wing 2/3 rds out from the fuse. These are in the shape of an L . The oldest style is the venturi tube mounted on the side of the fueselage convenientaly in the slipstream and unaccurate >=<. The third type is a 16" tube that protrudes out of the leading edge of the wing. Static ports are always mounted on the side of the fueselage. There usually are two. Some aircraft have them on the bottom of the aircraft typically less accurate during decent. Some pitot tubes are also a combination of static and dynamic. On the L shaped pitot tube the static port is on the bottom. On the tube style just before the leading edge there is a little flat spot where the static port is located. Beleive it or not. With the aid of gps airspeed altitude gauges are very accurate in reference when calculated for wind which the gps also knows when it has satellite weather linked. The gauge that fluctuates and takes time to come in is the VSI.

 

[mugaliens]

There was another thing I was wondering, the different airspeeds. If I understand it correctly, IAS is what is displayed on the airspeed indicator in the cockpit (using v = sqrt ( 2 * (total pressure - static pressure) / rho ))), CAS is IAS corrected for positioning errors (like the one you just explained, I suppose).

Iced Tea is a Pretty Good Drink! In airmen's terms, I --> C --> E --> T, and PGD stands for Position, Compression and Density.

In somewhat of an ad-hoc equation format:

I +/- (position adj) --> C - (compression adj) --> E + (density adj) --> T

Now, some sources say EAS is CAS corrected for compressibility.

Exactly.

But another says that EAS is the speed at sealevel at which the dynamic pressure is the same as the dynamic pressure for TAS at the plane's altitude.

That may be, but I've never heard it put that way before.

Compressibility is a factor of both velocity and altitude. Clearly, the greater the velocity, the greater the compressibility. However, altitude has an effect, as well, for the greater the altitude, the less compressed the air is already, therefore the more easily it's compressed by velocity. So, for velocities equal to or less than 200 kts and altitudes at or below 10,000 feet, the compressibility factor is 1.00. 200 kts at 50,000 feet, however, require a factor of .93. Similarly, 500 kts at 10,000 feet requires a factor of 0.97. 500 kts at 50,000 feet, however, it's down to 0.84.

Some other source said that EAS is used for lower budget aircraft that cannot measure rho and hence use rho(sea level), which makes more sense than "correct for compressibility".

LoL, US Air Force aircraft must be "lower budget," as we have IAS guages, too, and a true airspeed check is one of of the many tasks performed in the first hour of flight, especially when flying across the pond. Of course we have an air data computer which feeds the nav systems. The ADC does the calculations electronically based on IAS, temp, and pressure. Still, we have to make sure the ADC is working, right? So we do a manual true airspeed check.

...so, if these are simply calculations, I assume that modern aircraft then display CAS instead of IAS?

No, they display IAS. In modern aircraft, the design is solid enought that the CAS is never off from the IAS by more than a couple of knots, so for all practical purposes (such as complying with ATC instructions) ithe difference is negligible.

Oh, and what do you mean with "Typically, the backup port uses the aircrafts cabin pressure"? Does this mean the static port is on the inside, or that instead there is no port but a direct connection from the cockpit to the airspeed indicator that "feeds" the static pressure?

For unpressurized cockpits, yes - it's indeed cabin pressure. For pressurized cockpits, the backup pitot static system is simply a second set of ports mounted on the skin of the aircraft, but usually in a different location. This is to prevent inadvertant damage to one set, such as a bird strike or icing, from interfering with the other set.