Supersonic shockwaves


Shock waves around supersonic airplanes, rockets or canonballs are a problem. This text describes four ways to decrease them.


Introduction
1. Moving at subsonic speed
2. Narrowing the body
3. Let the body have a sharp nose
4. The area rule
5. Make the air move on purpose




Introduction

An object traveling trough the air at supersonic speed will originate two strong shock waves around it.

The front of the object will briskly knock the air apart in order to take its place. The shock wave is the zone where the air is moving away.

That zone is very large, virtually infinitely large. In the whole universe some air will have to move apart a few inches or a few microns in order to let the body trough.

A symetrical phenomenon happens at the back of the object. The back of the object goes briskly away from the zone of space it was inside and leaves a vacuum. That vacuum will be filled by the surrounding air. And all the air around, away to infinity, will have to follow the movement. That zone where the air is busy moving back in place is the second shock wave.





A shock wave carries energy. Imagine the shock wave originated by the front of the object arrives on a windmill. Because of the pressure and the frontwards moving air the windmill will turn and produce electricity. The same will happen with the shock wave originated by the back of the object; the depressure and the backwards moving air will make the windmill turn too.

Always remember the energy the shock waves carry away was furnished by the moving.

Shock waves are generally considered a bad thing, for the two following reasons:



1. Moving at subsonic speed

The trivial solution to avoid an object generates shock waves is to make it move at subsonic speed. A speed lower than the speed of sound (300 m/s).

When a body is moving at subsonic speed, the air in front of it has plenty of time to travel along the body and go directly to the back of the body. This way no shock wave is originated. The air further aside from the object is not disturbed.





While the shape travels to the right, the air around it travels to the left.

It's like if you put the output of a weak blower aside the input of a little vacuum cleaner. The air coming out of the blower will go directly into the input of the vacuum cleaner, without disturbing the air a few decimeters further. The blower is the front of the shape, the vacuum cleaner is the tail of the shape.

So, no shock wave is orginated, no energy is lost.

The only reason why the object will loose a little bit of speed is because the air is shearing along the body. That brakes a little bit the body. The air that has sheared along the body will be a little bit heated. Just afther the body passed along, the air may even be turbulent. Turbulences calm down and turn into heat.

Note a supersonic body also is braked by the air shearing along, but this is of minor impact compared to the generation of the shock waves.

Here are summarized some fundamental differences between subsonic aerodynamics and supersonic aerodynamics:


Subsonic
Supersonic
The air flows on the average parallel to the direction the object is moving, along the object from the front towards the rear. It may also move aside, make turns... It flows directly from any zone it is pushed away from towards any zone where it is needed to fill back. (If the word "flow" makes you think about water, it is better to compare the air with honey rather than with water.) At high supersonic speeds the air is slammed away in a direction nearly perpendicular to the direction the object is moving.
The air is not compressed. The air is compressed in the zones where it is moving. Those zones are called the shock waves.
Practicaly, the moving object makes the air move only in its neigbourhood. The molecules in contact with the object skin do move with the object, then when you go away from the skin you quickly and gradualy enter in a zone where the air is moving in the oposite direction, and when you continue to move away from the skin the air moves slower and slower. At a given distance from the object you may say the air remains unmoved. The air is moved virtualy everywhere around the object. In theory, the total energy of the air moving away at an infinite distance is the same as the energy of the air moving away close to the body.
In a diverging nozle, subsonic air will slow down. It will accelerate in a converging nozle. In a diverging nozle, supersonic air will accelerate (that's the way rocket motors work (don't bother too much with that story about the hole that does not equilibrate the pressure on the opposite wall; that's only the main phenomenon for low yield motors. Modern space rocket motors work the supersonic way.)). It will slow down in a converging nozle.




2. Narrowing the body

The narrower the body, the less the air will have to move apart in order to let the body travel trough it. That's why supersonic planes are much longer and thin than subsonic planes. Compare a Boeing 747 and a Concorde...

In other words: the hard work for a supersonic body is to knock the air apart at the front. The more cross section the body will have, the more air will be obliged to move apart in order to let it trough.

Yet, in first approximation, the length of the body is of no importance. Once the air has been moved apart, you may shove trough it any length of body you want.

Thus, it is highly profitable to make the body cross section be little, yet that's of no great importance if the body is very lenghty.

That's just like for a nail: provided they have the same diameter, long nails are not harder to hammer a few milliters more trough the wood than short nails. The whole work is to make the wood be crunched apart by the nail point. Then no matter the length of nail that follows.

Note you should not make the body be too narrow and long, for two reasons:



3. Let the body have a sharp nose

Did you ever move a spoon trough ice cream? The ice cream accumulates in front of the spoon and when you lift the spoon out of the ice cream you have a big piece of ice cream, a lot larger than the spoon diameter.

The same happens for a blunt shaped supersonic body nose: a pack of air will accumulate in front of the nose and will behave like if the nose held an umbrella open in front of it. An umbrella much larger than the body diameter. That's of course an important brake.

More physically said: the air is thrown in front of the nose, accumulates and forms a high pressure layer that overflows aside from the nose along the body. That high pressure layer exerts a huge force on the nose front surface, braking the body.

To avoid the air pack in front of the nose, the nose must be sharp-shaped. Then the air will gently be smashed sideways.

The same is true for a nail. Sharp pointed nails are easier to hammer than blunt nails. (Yet blunt nails are easier to remove aftherwards because the wood has been more destroyed and pushed away when the blunt nail entered.)



4. The area rule

The area rule is that along a supersonic body the cross sections should always have the same surface. (Except for the nose, of course, where the cross section surface smoothly rises, and for the tail, where it decreases to null.)

In order to explain correctly the area rule let's first suppose two rockets A and B.

Rocket A has the shape of a perfect pencil, with a sharp nose just like a pencil point.

Rocket B looks like rocket A, has the same volume, length and a sharp nose. Except for one thing: its body is of irregular diameter. Along the body the cross section increases and decreases constantly.





When rocket A and B travel trough the air at subsonic speed, rocket B is braked as much as rocket A. In fact a little more because its maximum cross section is a little larger than A and because the path for the air along its body is a little more complicated, but the difference is not outstanding. At every place along the B body where the cross section increases the air has plenty of time to move to any place where the cross section decreases. It may move sideways, backwards, forwards, to a remote place at the end of the rocket, no problem... it's just a local little flux of air.

But at supersonic speed the situation is completely different. At every place along the B body where the cross section increases the air is smashed away and forms a push shock wave that travels away. At every place where the cross section decreases the air is violently sucked back to place and forms a suck shock wave that travels away.

At every place where the section increases the rocket is pushed back severely by the air and at every place where the section decreases the rocket is sucked back severely by the air. Here is a drawing of rocket B travelling at mach 1:





At supersonic speed, rocket B is monstruously braked by the air. Maybe ten or twenty times more than rocket A. What's more it sends away trough the air a huge amount of energy under the form of shock waves. A sort of sandwich of pushing and sucking shock waves.

Now for sure you understand why the cross section should be the same everywhere. Rocket A, that obeys that rule, just generates the minimum and unavoidable quantity of shock wave: at the front in order to enter the air and at the rear because the air comes abruptly back in place.

That's okay. Yet something very important has now to be said. in order to illustrate it let's suppose we want a rocket to carry a pod. A sharp cilinder latched aside to the rocket body�:





The pod nose will generate a shock wave, and so will the rear. Thus the rocket motor will have to push harder, because that pod the rocket carries is braked by the air.

Well there is a magic solution to make the pod no more brake the rocket! Simply let the rocket body be narrower there where the pod is situated�:





At the place where the pod nose begins the rocket body decreases a little bit of cross section. Then where the pod ends the rocket body inflates back to its normal size.

The decrease in rocket cross section will generate a sucking shock wave that will compensate the pushing shock wave generated by the pod nose. The pushing shock wave generated by the pod nose will act on the rocket body and compensate the sucking effect of the air. Reciprocally, the sucking shock wave generated by the rocket body will suck away the air that would otherwise be pushing back the pod nose. The same happens at the end of the pod, symetrically.

Now the pod no more brakes the rocket! Every push effect is compensated by a suck effect originated laterally of it, and vice versa.

What is the exact amount of surface the rocket body cross section should decrease in order to compensate exactly for the presence of the pod cross section? Well simply the same amount as the pod cross section surface. So, just consider the rocket cross section and the pod cross section as a whole and make the total surface be a constant number along the rocket body.

It is by following that rule, the area rule, that engineers first managed to build effective supersonic planes. If you cut out their planes in slides and if you measure the total surface of each slide, including wings length and tickness, cockpit, motors... you will notice the total surface of every slide is the same. Except for nose and tail.

So, it is possible to build a rocket C with an irregular cross section yet with no increase of the brake effect. Indeed the cross section is allowed to change shape along the rocket body, provided the surface of each cross section remains a constant. You may for example take a straight rocket like rocket A and push gently on a part of its side so it flattens where you push and widens sideways. You get an elliptical cross section where you pushed, yet with the same surface as the circular cross section before. You may do that on several places along the rocket body and make it look a little bit like rocket B, yet it will be braked no more than rocket A when travelling at supersonic speed.



5. Make the air move on purpose

You can make air behave around a supersonic body exactly the same way it behaves around a subsonic body (chapter 1).

Therefore you must not rely upon the air to make that correct movement. You must force the air to do that movement. Like if you had thousands little arms taking the air in front of the body and bringing it quickly to the back.

This has been depicted by M. Jean-Pierre Petit, who also gave a way to achieve that seizure on the air: magnetohydrodynamics.

If you ionize the air in front of the body, drive a huge current trough it, and make the body generate a strong magnetic field with the apropriate shape, the air will be forced to shreak around the body, from the front towards the back.

This way, the body will not generate any shock wave while traveling trough the air at supersonic speed.

Successful experiments have already been done into salt water, allowing little bodies to travel very fast trough the water. But those little body needed external magnets or power sources. Bodies traveling trough water by their own are very slow. This way to avoid shock waves needs far too much energy to be useful in the actual state of the technology.




Eric Brasseur  -  30 March 1997       [ Homepage | eric.brasseur@gmail.com ]
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