Shock waves around supersonic airplanes, rockets or
canonballs are a problem. This text describes four ways to
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
An object traveling trough the air at supersonic
speed will originate two strong shock waves
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
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
- They make the object loose speed. Indeed,
in order to knock the air away the front of the
object constantly must exert a huge force on the air.
And the back of the object is pulled back because it is
sucking air. Those two phenomenons
make the object slow down
quickly. To keep a
constant speed it must use a rocket motor or a
reactor. That rocket motor
or reactor will have to be a big and strong one,
consuming a lot of fuel. It must constantly
compensate the energy the object loses. (That lost
energy travels away from the object through the two shock waves.)
- Those shock wave are a nuisance for the
neighbourhood. Remember the millions of windows
military airplanes have broken by flying at
supersonic speed too close to the ground. A
window pushed away or sucked by a shock wave
breaks like hit by a brick.
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:
2. Narrowing the body
|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.
space rocket motors work the supersonic way.)).
It will slow down in a converging nozle.
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
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
- The narrower the body, the longer it will
be, in order to keep a same volume. It will
thus get a lot of side surface. Air shreaking
along the surface will brake the body. Having
too much side surface is thus not a good idea.
What's more the turbulent air near the surface
will make the body behave like if it was larger,
like a second invisible thick skin. A compromise
has to be found: the body is made narrow,
but not too much.
- Narrow bodies are more fragile. They bend.
So they must be build heavier, with more
materials, in order to make them resistant.
Being heavier is for sure not a good thing
for a rocket or an airplane.
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
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
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
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
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
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
30 March 1997