# Do speed and density exhibit a linear relationship?

Does speed and density scale linearly? Say you’re going 500mph, and speed up to 600mph. The density of the air will decrease.

Now if you’re going 1000mph and speed up 100mph, does the density decrease the same amount?

What is the reasoning behind the answer?

My guess of what happens with density at higher and lower speeds is the following (my guess is that it's a non-linear relationship) : The air density doesn't change much until you reach Mach ~0.3, where Bernoulli's equation isn't valid anymore, so the density can't change but so much, or Bernoulli's equation would be false, even below Mach 0.3.

When you go faster, there are less air molecules to 'bounce' off of the surrounding body and each other (because at high speed, the surrounding air is less dense), so changing speed doesn't do as much as it would at a lower speed, if that makes sense. (I might be wrong about some of those statements.)

I think if I explain my guess of why density doesn't change much up until Mach 0.3, it might clarify things. So if you have normal-density air (like still air at room temp) and you start to speed it up, a few things happen.

The air molecules bounce off of each other less, because they all have a forward speed component now, and they 'bounce' less on the surrounding container/body, both creating a lower density air. Doing this at lower speeds, there are more molecules, and because there are so many, speeding up doesn't prevent the 'bouncing' as much as it does at higher speeds. (Again, I might be wrong about some of those statements.)

• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Aviation Meta, or in Aviation Chat. Comments continuing discussion may be removed. Jan 9 at 18:38
• I've moved the comments to chat, please continue the clarification discussion there. Once it has been clarified whether density or pressure is meant and whether we are looking at total, static or ram pressure / density, the question should be updated and flagged for reopening. Jan 9 at 18:44

## 1 Answer

According to NASA: "As an aircraft moves through the air, the air molecules near the aircraft are disturbed and move around the aircraft. If the aircraft passes at a low speed, typically less than 250 mph, it is observed that the density of the air remains constant. For higher speeds, some of the energy of the aircraft goes into compressing the air and locally changing the density of the air. This compressibility effect alters the amount of resulting force on the aircraft since the aerodynamic force depends on the air density. The effect becomes more important as speed increases. Near and beyond the speed of sound, about 330 m/s or 760 mph at sea level, small disturbances in the flow are transmitted to other locations isentropically or with constant entropy. Sharp disturbances generate shock waves that affect both the lift and drag of the aircraft, and the flow conditions downstream of the shock wave." NASA

Updated for poster's request for "why"... Unlike solids and liquids, a gas's molecules are loosely bound and have considerable space between them. This makes the air around us easily compressed. As an object travels through air, the air's molecules are prevented from moving out of the way do to friction (and momentum). As an object moves faster, more molecules stack up in front of it and are kinetically forced closer together; an increase in molecules for a given space causes an increase to it's density and relative pressure.

At mach one, the air is prevented from moving out of the way at the same speed as sound energy. Sound energy plus the density/compression causes a sharp pressure gradient we know as a "shock wave".

• Oh okay, thanks for your response. So I have a guess why the density doesn't change much below ~250 MPH, but I don't know for sure, so could you possibly explain that to me? Jan 12 at 18:23
• Why? Because it's been measured. Jan 12 at 19:27
• I edited my question and added the last section to it, which might help you see where I'm coming from. (about the density below Mach 0.3 part) Jan 13 at 3:32
• Density is not linear to speed - there is little density increase below 250mph but disproportional to increase with speed. For example the density at 500mph is more than twice as much as 250mph. And the density at 2000mph is more than twice 1000mph. The disproportional density is primarily due to the non-linear property of friction (as explained above). Jan 13 at 19:42
• @jwzumwalt Ah okay, thanks for your help. One last thing : do you believe that my guess(es) in my question is correct? (I made a few edits and added some things) Jan 13 at 23:53