# What is the "compression ratio" of air hitting the nose?

Sorry but I don't know how to accurately phrase this question. I want to know how much compression results from air hitting the nose of an aircraft.

I'm interested in the traditional airliners (Mach 0.85, blunt nose, like B747 or A320), as well as the supersonic stuff like Concorde and even Mig-31.

Is there an equation for this? Presumably with cross section area and some kind of coefficient of form drag. I'm looking for a density and/or pressure change.

I want to know if this is significant, like if the aircraft actually has to do a lot of extra work to overcome the greater density in the nose air. But there are actually several reasons. I want to calculate how much heat arises from the adiabatic compression, which will let me know if some kind of active cooling is required for a given material. I want to know if the increased density of the nose air actually changes the general drag equation, like if you have to put in a higher density value when just calculating the fuselage drag. I want to know what possible boost you can get from the "ram effect" such as from a ramjet.

In this question, all I'm really asking for is the compression ratio...or change in density, or change in pressure...sorry I don't know which one is more accurate. If I just have that, then I think I can answer the rest using other equations I know of.

I wanted to explain myself in case this appears too broad or too xyz thing, sorry can't remember that term either. Hopefully someone will know an equation that can answer this. Equations give hard numbers, so they're always better than relative adjectives like "larger", "negligable", etc.

Also, if someone can suggest tags, please do so. Couldn't think of anything better than "drag".

I think what you seek is called the stagnation pressure, which is the pressure rise experienced in a given parcel of air if all the kinetic energy associated with that parcel's velocity were to be converted without losses into potential energy (stored work) of compression according to the ideal gas law. The equation for stagnation pressure is

$$\frac{P_\text{stagnation}}{P_\text{static}} = \left( 1 + \frac{\gamma - 1}{2} \times M^2 \right) ^ \left( \frac{\gamma}{\gamma - 1} \right)$$

where $$\gamma$$ is the ratio of specific heats for air and $$M$$ is the Mach number.

• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review Sep 1 '19 at 0:55
• edited to include equation. -NN Sep 1 '19 at 1:11
• OP did not specify stagnation pressure in an engine. Sep 1 '19 at 17:16
• I'm interested in air hitting the leading edge of an object, like the nose or wing edge. I don't see how to use the equation, tho, because it doesnt have any cross section area or coefficient of drag. Surely the nose of a B747 has more stagnation pressure than the nose of a tiny business jet at the same speed? Likewise for the leading edge of a wing versus the big nose. Without cross section area I don't see how it can be trustworthy. Maybe stagnation pressure is not the right thing after all? Sep 2 '19 at 2:29
• @DrZ214: Stagnation pressure can be found at only one point (the stagnation point, obviously) so there is no area on which it acts. Pressure drops when you move away from the stagnation point, so in reality you will have to integrate with a pressure gradient when calculating drag on the aircraft nose. But stagnation pressure is real: It limits the top speed of blimps to the point where internal pressure equals stagnation pressure, or the blimp's nose will deform. Sep 2 '19 at 6:05

The simple answer for sub-sonic aircraft is zero. Air does not compress significantly until shock waves start to form.

Pressure changes with speed (as per Bernoulli's principle) but density can be treated as constant.