# Would air having an infinite speed of sound be ideal?

Hypothetically, if aerodynamicists had the opportunity to somehow raise the speed of sound in air to an infinite level so that air was no longer compressed, how would this affect aircraft related aerodynamics? Are there cases a higher speed of sound would be helpful rather than a hindrance?

Would subsonic aircraft designs be able to fly much faster without design changes?

Would we be able to design axial compressors with much higher pressure ratios per stage?

Perhaps much higher thrust could be generated from the same size propeller?

Are there cases where this would not be desirable? Such as spacecraft re-entry for instance?

• I don't think they reference a Mach speed in outer space. Commented Jan 27 at 19:40
• To "somehow raise the speed of sound in air to an infinite level so that air was no longer compressible" sounds more like WorldBuilding than Aviation to me.
– Ralph J
Commented Jan 27 at 21:19
• @RalphJ You’re right, however I feel asking what if questions can increase our understanding. It is taken for granted that air compresses, what if it wasn’t compressible? Would this be a much better world for the aerodynamicist? Commented Jan 28 at 15:46
• @usernamechecksout wouldn't that be water? Commented Jan 28 at 16:14
• @AadirajAnil Water is compressible, just less so. Generally the less compressible the medium the less time it takes for “information” to pass through it. Commented Jan 28 at 17:24

I think there's some misconception, and I hope you correct me if I'm wrong, the title is "infinite Mach", but you're saying you want to raise speed of sound to infinity, this means mach no. is zero, because $$M = \frac{v}{a}$$.

But why do you think decreasing compressibility is useful in aviation?

However, if I understood your question then the answer is: no, subsonic airplanes won't fly much faster if speed of sound $$a=\infty$$, actually they won't be able to fly at all. As people reffered out in the comments, a matter with infinite speed of sound is more likely to be a solid rather than a fluid. Of course, solids don't have infinite speeds of sound, but they're considered to be so in the context of studying fluid mechanics, because comparatively, speeds of sound in solids is much much higher than in any normal fluid.

Another way to think about it is: assuming $$a=\infty$$ might be somehow similar to assuming the velocity of the airplane is zero $$v=0$$, because both assumptions lead to zero mach no. $$M = 0$$ which means there's no motion of the body inside the domain that was once considered as a fluid.

• Thank you for your answer. I realize that my title was asking the wrong question. I do mean an infinite speed of sound, not Mach number. I disagree that Mach=0 means no motion of the body. A Mach of 0 would mean there are no compressibility effects, not 0 motion. Mach isn't a measure of velocity. Commented Jan 28 at 20:09
• Welcome to Aviation SE! This answer's good enough to be your hundredth, not your first :-) Commented Jan 28 at 20:13
• @usernamechecksout I agree that mach number is by definition: a measure of compressibility, but may be there's something I don't understand, why does a higher speed of sound mean higher velocity? What I know is: I can only play with two things (independent variables in our context): velocity and speed of sound, so if I change the speed of sound of a fluid, this means that mach no. (dependent variable) changed, but it doesn't mean that velocity of airplane changed at all, because it's still independent of speed of sound. Again, correct me if I'm wrong🙏🙏 Commented Jan 29 at 23:26
• @CamilleGoudeseune you're too generous sir, thank you a lot🙏 Commented Jan 29 at 23:30
• @أحمدصلاح A higher speed of sound wouldn't change velocity. It only changes the ratio of velocity to the speed of sound. The lower the ratio the lower the Mach number, or in other words the compressibility. V could be any value you choose. If you're solving for V of course it wouldn't make sense for Mach to be 0 otherwise infinity*0=undefined velocity. Suggesting the use of infinity may have been a mistake on my part. I really meant "infinite" in more of the common english definition not the mathematical one. I am learning all of this as we go so correct me if I'm wrong. Commented Jan 31 at 2:13

Hypothetically, if aerodynamicists had the opportunity to somehow raise the speed of sound in air to an infinite level so that air was no longer compressed, how would this affect aircraft related aerodynamics?

The aerodynamics would just look like incompressible aerodynamics i.e. just like any aerodynamics happening at Mach numbers smaller than 0.3. There wouldn't be any difference in respect to what it is already known about that particular branch of aerodynamics.

If you want to keep the fluid incompressible (Mach number <0.3) but travel anyway faster, you just have to increase the speed of sound either by playing around with the fluid and/or its temperature: this is something normally achieved in "cryogenic wind tunnels".

Obviously getting rid of all the side effects of compressibility (wave drag, shift of the aerodynamic centre, shockwaves,... ) would have, in general, a net positive effect, mainly less drag.