Wednesday, 24 August 2016

Pressure Altitude and Density Altitude

When asked what pressure altitude is or what density altitude is most pilots will inadvertently dodge the question and instead tell you how to calculate pressure altitude or how to calculate density altitude. This leaves unanswered the questions: What is density altitude? What is pressure altitude?

Here are the answers to those questions:
Dude, Pressure altitude is the altitude in the standard atmosphere at which you would find the pressure in question (usually the observed pressure).
We calculate pressure altitude for an airport by subtracting the current altimeter setting from 29.92 and multiplying the result by 1000. We then add this result to published field elevation
The altimeter setting in Prescott is 30.16 what is the pressure altitude?
Answer: (29.92 - 30.16) * 1000 + 5045 = 4805' MSL

This means that the pressure you are observing in Prescott will be found at an altitude of 4,805 feet in the standard atmosphere.

Now on to Density Altitude
I'm just gonna say it.
Density Altitude is the altitude in the standard atmosphere at which you would find the density in question (usually the observed density).
We calculate density altitude by correcting pressure altitude for non standard temperature using an E6-b (or something fancier).

To better understand Density Altitude, consider the following scenario, which actually happened once:

1. You are kidnapped by a tribe of five-legged aliens.

2. Using magical technology they suspend you at some point in the atmosphere and give you a magical density measuring device.
3. They ask you what your altitude is and place bets on how close your guess will be to reality.
4. They inform you that if you're more than ten percent off that they'll execute you by feeding you to the ravenous Bugblatter Beast of Traal.

...You read the output on the density measuring device and find ambient density to be .9 kg per meter cubed. You bust out your smartphone (which still has service) and follow the above links to a table of the standard atmosphere. You find that in the standard atmosphere a density of .9 kg per meter cubed occurs at about 3km altitude which is 3,000 meters high. You tell the aliens that you are 3,000 meters high. They are Imperial Aliens and demand the answer be given in feet. Being a very crafty pilot you know to multiply 3,000 by 3.28 to get feet. You bust out your smartphone again and multiply 3,000 by 3.28 to get 9,840 ft, you tell the aliens that you are at 10,000 feet MSL.
The aliens acknowledge that you are correct but decide to feed you to the Bugblatter Beast of Traal anyway. You die with a complete understanding of what density altitude is and how to calculate it.

Monday, 22 August 2016

Static Pressure and Dynamic Pressure

When explaining lift and various other aerodynamic and meteorologic phenomena it is vital to understand the difference between dynamic pressure and static pressure.

We feel dynamic pressure all the time, when we feel it, we call it wind. If you blow on your hand right now, you will feel dynamic pressure.

To get technical, dynamic pressure is equal to one half of density times velocity squared.
  • q = Dynamic Pressure
  • ρ = Density
  • V = Velocity
Dynamic pressure acts in only one direction, the direction of the velocity.

At sea level, static pressure is usually many times the strength of dynamic pressure but we rarely feel it. That's because the only things we feel are forces, and forces are caused by differences in pressure. And usually we are at the same pressure as the environment, which is about 14.7psi at sea level and about 12.2psi at 5,000 feet. If you are at sea level it's not just the air that's at 14.7psi, it's every cell in your body, it's every molecule that you are composed of that is at this pressure.

The immense power of static pressure, which unlike dynamic pressure acts in ALL directions, is only apparent when it interacts with a much higher or much lower pressure, such as the near zero pressure of space or the very low pressure experienced by aircraft cruising at high altitude. Below is a truly disgusting scene from the movie Alien (no seriously, don't watch it if heinous disembowelment grosses you out) where the immense forces created by static pressure acting against a vacuum suck the alien out of the spaceship. There are similar scenes in Star Wars and Star Trek but I couldn't find clips of them on YouTube.
Now it isn't only in gruesome space movies where effects of static pressure are demonstrated. If you've ever left toothpaste or contact solution or some other bottle of liquid in your car while traveling up to high elevation you've probably noticed the pressure escaping when you opened that bottle. Additionally if you have a sinus blockage or inner ear infection while travelling by car or aircraft you'll have felt that pressure in your sinuses or ears (which can be quite painful). Additionally if you've ever swam to the bottom of a pool you have probably felt the extra static pressure added by the water on your ears.
One last way to try to understand static pressure. Sea level pressure is 14.7psi, the average human adult has about 800 square inches on one side of their body, that means that if one side of your body had normal sea level pressure on it but the other side was somehow exposed to the vacuum of space that there would be a force of 11,760 pounds blowing you into space. You get 11,760 pounds by applying 14.7 pounds of force to each square inch of this average adult body. 

So there you have it. Static pressure and dynamic pressure, post questions and corrections below.

Sunday, 21 August 2016

How a Wing Produces Lift (FAA Edition)

It can be a challenge to explain how lift is created while doing all of the following:

1. Use Bernoulli's Theorem (which is what the FAA likes).
2. Avoid telling obvious falsehoods (which is what flight instructors like).
3. Be vaguely comprehensible.

Below is one explanation which meets all three criteria.


Because of the shape of the wing and the Angle of Attack, air flows faster over the top of the wing than over the bottom of the wing. In this sentence is hidden all the complexity and mathy nonsense that scares people away from looking into how lift is created, I'll re-state it. Because of the shape of the wing and the Angle of Attack, air flows faster over the top of the wing than over the bottom of the wing.
Now let's talk about types of pressure. Total pressure, is always equal to dynamic pressure plus static pressure (in subsonic ideal flow) ...which is illustrated by the below equation.
Now dynamic pressure is proportional to velocity, so if velocity goes up, dynamic pressure goes up. As we stated above, air flows faster over the top of the wing than over the bottom of the wing which means there is greater dynamic pressure on the top of the wing than on the bottom

Because total pressure must stay constant, the higher dynamic pressure on the top means static pressure must be lower on the top. Conversely, the lower dynamic pressure on the bottom means that static pressure is higher on the bottom.
Dynamic pressure only acts in one direction, the direction of the arrows above and below the wing, which means it does not exert any force on the wing. This means that only Static Pressure exerts a force on the wing.
So only static pressure exerts a force on the wing, and dynamic pressure is higher on the top of the wing than on the bottom of the wing ...which means that static pressure is higher on the bottom of the wing than on the top of the wing. This is lift. Lift is the difference in static pressures between the top and bottom of the wing.

For a more complete explanation watch this lecture

Sunday, 7 August 2016

The True Story of P-Factor, for Pilots

P-Factor, or Propeller Factor (or asymmetric blade effect or asymmetric disc effect), is an important aerodynamic phenomena for pilots to understand, at least it is if your plane has a prop.

P-Factor is often explained to pilots in silly ways using false analogies (No! the blades do not have mouths, one does not take a bigger bite of air than the other!). At AirCrafty we absolutely detest false analogies and believe that anyone using them should be mailed third class to a dark place between two stars. What follows is the True Story of P-Factor:


Below is an image of an aircraft whose 2-bladed prop has one blade (the descending blade) coming straight out of the screen and the other blade (obviously the ascending blade) going back through the screen. The dashed lines going through each blade represent the chord lines of each blade.
Angle of Attack (AoA), as all good pilots know, is the angular difference between the chord line of an airfoil and the relative wind. If the above prop began spinning while the aircraft was stationary on the ramp the Angle of Attack (AoA) would be the same as the angular difference between a vertical line and the chord line as shown below:
But if the aircraft were moving forward, finding out where the relative wind was coming from would be a little tougher, we'd have to add the velocity of the aircraft to the velocity of the prop as shown below:

Don't be intimidated by the busy graphic, stare at it for five minutes and it will make sense (...because the aircraft is moving forward the wind hits the prop from a more forward direction reducing the angle of attack on the prop blade by an amount equal to the BHA). 
Bonus! BHA stands for "Blade Helix Angle" a term you can use to impress some people at the public pool later today (the blade helix is traced by the prop tips of this C-130).

Now go watch this 3 minute YouTube video, the guy's accent is great and it'll help you solidify your grip on things before we move on.

OK so far we have an angle of attack on the blade but no P-Factor. Now we'll pitch the aircraft up and continue to fly straight and level (neither climbing nor descending) ...slow flight style; as we do this, P-Factor will emerge in mysterious fashion like consciousness emerging from a brain.

You've probably already gazed furtively down at the below graphic. Be intimidated by this busy graphic. Panic, hyperventilate, go through the five stages of grief, then recall the Nietzschen aphorism your dad taught you. Look! the busy graphic didn't kill you! Therefore you're stronger. With this new strength you will now understand P-Factor como un jefe.

There's a couple things going on here:

1. Because we pitched up, the velocity of each blade is no longer perpendicular to the velocity of the aircraft. This means a large component of the aircraft's velocity adds to the descending blade's velocity. For the ascending blade there is now a component of the aircraft's velocity that subtracts from the blade velocity. The addition of a component of the aircraft's motion to the descending blade and subtraction of a component of the aircraft's motion from the ascending blade is the first part of P-Factor. I left the old aircraft velocity vectors that are perpendicular to the blade velocity vector on the above graphic and made them a faint green color so you can still see how things were before we pitched up.

2. I also left the old relative wind vector for the descending blade on the above graphic (but left it off for the ascending blade) and made it a faint blue color, it is mostly hiding behind the new relative wind vector of the descending blade. Notice that the old relative wind vector isn't just shorter (and therefore the relative wind is slower) but it's also at a slightly different angle than the new relative wind vector (the not-faint blue arrow). This new relative wind vector is closer to vertical which means the BHA has been slightly reduced which means the angle of attack has been slightly increased. On the ascending blade the change in angle of attack is negligible in most cases (more on this in the Technical Section below). The increase in angle of attack on the descending blade combined with the negligible change in the angle of attack on the ascending blade is the second and final part of P-Factor.

I'll re-state it all together here...If the relative wind is not perpendicular to blade velocity, a component of the aircraft's velocity adds to the descending blade's velocity and subtracts from the ascending blade's velocity; at the same time, the angle of attack on the descending blade increases while the angle of attack on the ascending blade changes a negligible amount. The descending blade therefore has greater velocity and greater angle of attack than the ascending blade, therefore it creates more thrust than the descending blade, this asymmetric production of thrust causes a yawing moment (a yawing moment which is normally to the left and needs to be counteracted with right rudder), this yawing moment is P-Factor

And that, is the true story of P-Factor.

If you want to be able to quantify the affects of P-Factor rather than just understand it conceptually, and if you want to learn what "PAAoA" stands for, then continue on to the technical section below.


PAAoA stands for Prop-Axis Angle of Attack. It is the angular difference between the axis about which the prop spins and the relative wind. The PAAoA, in combination with aircraft velocity and prop velocity, determine the magnitude of the moment we call P-Factor. The relationship between these three quantities is shown below:

The black dashed line is vertical, the relative wind (RW) velocity can be calculated using the Law of Cosines, C^2 = A^2 + B^2 - 2ABcos(c) modifying this for the present triangle and solving for relative wind gets us:
Once we have relative wind the BHA can be calculated using the Law of Sines. I won't bore you with the Law of Sines, here's the resultant equation solved for the BHA:

Now I'd like to curse Blogger four times for not building an equation tool into blogger and constantly monkeying with settings causing mathjax and various other LaTeX readers to be unreliable. Curse you Blogger, Curse you Blogger, Curse you Blogger, Curse you Blogger.