The sonic boom

Really! wow that's cool.. To bad he didn't mention you in his research paper.

I still think he's wrong..

I posted the same question on a science forum I go to. Maybe some the the crazy smart guys there can figure it out...

skip

Nice Article!!! But Goriely wrote a lot more, it´s very intresting!!!

The only aspect they have calculated is the shape of the whip. With a small whip the loop is very close and a long whip has a bigger loop. The flexibility of the whip dictates the loop size too. You only talk about the end (the cracker) and not the whole whip. They studied the whip but not the end and so you talking about two different topics.

The whole whip is really difficult to explain. The thong and fall is studied enough by goriely(the effect of the shape and the motion). But the cracker and the sound of it is a misteria till today. But in the following text are my thoughts about it. Please do your own experiments with it.

Use some crackers with an very elastic material(like rubber use fine fibres), and another which has a low tension module (like kevlar). By the same size it will crack different. This is the factor tensile. The loop get´s longer and the crack is not so sharp. You can amplify the effect with a elastic fall (try it with a poly fall and then with a kevlar fall, but beware of the weight)

Use one like nylon with fine fibers and one like poly with bast fibers. The poly fibers are not so flexible like the nylons so the tuft will be not the same. This is factor fibres.

The next factor is the shape. It might seems to be unbeliveable, but not only round crackers were used. The Karbatschenknaller use 50mm ribbons which has the same weight than a 3mm round cracker. The tuft is also bigger, and so the energy of the whip is shared to more air. The cracker reaches not the speeds like a round cracker but it lasts for a sonic boom. The crack is deep and loud.

The last 2 factors are the temperature and the tensilestrength. If the material is to weak the tuft(or the cracker itself) will vanish to thin air. Is the material strong enough you can reach speeds over Mach 2,5 and there the temperature is high enough to melt the tips(only 0,1-1mm) of the tuft. So they are thicker and break by the next crack. The cracker gets fast shorter. The crack itself sounds high but not so loud, because more energy were converted in heat. For this problem you can use the aramids like vectran or kevlar which has a meltingpoint of over 400°C.

thx for bringing this up again, i really like the topic.

We still are comparing apples and oranges.
And i am pretty sure that i also fail to put all together, but sometimes it is the fun wandering how it works.

In my opinion the profersor is right with his math's. A whip has a complex motion, there is the trow and what he call's the loop.
I prefere to call the last one a wave. The wave will accelerate and because of the decresing mass (and no energie lost) this will be the energie source that causes the actual crack. In the mean time the whip travels to where you have been steering it, carring the wave.

The video shows clearly that the cracker makes a quick movement at the moment that the wave can not be transmitted any longer by the whip (whip, fall and cracker must been seen as one and the same for carring the wave) The wave come's off the whip and cracks.

In sailing i learned that some parts in a (water)wave are travelling with twice the speed of the wave itself (motion in motion).

When the wave comes off the whip all remaining energie is transformed in speed. I am sure the proffesors math's will show a factor 2 compaired with the last speed of the wave.

for seeing the movement of the cracker i like the part with the firewhip at about 30 seconds of the vid.

quattro made a few good statements and when using elastic materials there is a great energie loss

in the cracker the energie is spread over all the fibres and creating lots of sonic booms.
The difference in sound is also complex, a large whip will have a slower wave and a deep boom and a small signal a higher sound???
quattro mentioned the size of the loop / wave, i have no answer.

I will do some private research this afternoon and enjoy myself

Andree

I will try and find the rest of the article but, the end of the cracker is what causes the sonic boom, not the loop.  The loop is certainly an effective means by which momentum can be transfered to the cracker tip.

It is the handoff of momentum that make whips work.  Momentum is mass multiplied by velocity.

As you start to throw the whip the velocity is low because, the entire mass of the whip is participating.  As the whip start to straighten out in front of you, a loop is formed.  As the loop travels down the whip, the heavier back end of the whip is coming to a stop.  The loop continues to transfer momentum to the lighter front end of the whip.

This process continues until the only thing that is moving is the tip of the cracker.  Since momentum is conserved, the velocity must increase.  Because the end of the cracker is so much lighter than the entire whip, its velocity is greater than the speed of sound in order for momentum to be conserved.

There are loses due to internal friction in the plaiting, air drag and other phenomenon.  This is why a well made whip has a more powerful crack.  It is simply more efficient than a lesser whip, resulting in less loss of energy.

Chris

Since I do have a rather extensive background in physics, shock wave production and supersonic fluid dynamics, I will try my best to explain how the whip crack occurs.

Summary of the production of the 'crack':
The initial velocity of the whip multiplied by its mass has initial momentum. As motion continues down the length of the whip momentum is conserved (minus some frictional losses). Near the tip the velocity is greatly increased to conserve momentum. The popper carries a packet of air with it due to the no-slip boundary condition. If the speed of the popper is sufficient it will create a 'whizz' sound which is the development of a Kármán vortex street. If the popper suddenly changes momentum, the packet of air that the popper carries with it will create a separation zone. If the change is fast enough, a separation bubble of low pressure occurs. When the air around this separation bubble pushes on the separation bubble, the bubble will collapse and the impact of air molecules will dissipate it's momentum in a wave.
If the separation velocity of the air packet, or inertial fluid drag pocket, and popper exceed the speed of sound, a cavitation bubble occurs between the two because the air molecules cannot move fast enough to fill in the space between them. When a cavitation bubble collapses a sharp 'boom' is heard because there will be a sharp increase in air pressure upon collapse (this pressure jump is a step function).  That step function in air pressure dissipates out wards and is the sound of the crack when it hits the ear drum. When the popper rotates while creating the cavitation bubble, as in looping cracks, this generates vorticity around the bubble which aids in its growth, and produces and even louder crack. Think about the air around the cavitation bubble spinning like on a merry-go-round and the centrifugal reaction carries the cavitation boundary outwards.

The more fluffy the popper the bigger the cavitation bubble if the velocity is the same. A fluffier popper also causes more drag and slows down the end velocity.
Even if you do not break the sound barrier, a small separation bubble can collapse fast enough to sound really close to a crack.
The larger the relative separation velocity of the popper and the inertial fluid drag pocket the larger the cavitation bubble.

Why certain whip cracks are louder than others:
As we all know, certain cracks are louder than others. They can fit into 4 categories:
Termination of Linear Momentum - e.g. Flicks
Reversal of Linear Momentum - e.g. Towel cracks
Termination of Rotational Momentum - e.g. Cattlemans
Reversal of Rotation Momentum  - e.g. Overheads

For cracks using the same whip, this is the order from quiet cracks to loud cracks. This is because when a the momentum of the whip terminates, the cavitation bubble it carries separates at the same velocity as the end of the whip prior to separation. When we reverse the momentum (pull back on the whip) the inertia of the cavitation bubble (more accurately the mass of the air around the cavitation bubble) carries it foward while the cracker moves backwards, so the relative escape velocity of the cracker and cavitation bubble is increased. The same is true for when we have a loop in the crack, the main difference is that the bubble  developed is extend in a linear fashion or created an expanding development of vorticity with added angular momentum. Imagine the difference of a single gram of gun powder in a closed tube versus 2 grams (linear + angular) of gun powder not in a tube being set off.

Much more complicated mathematics is involved, but if you think about the cavition bubble moving away from the popper at with a certain amount of momentum, the following occurs:
Termination of Linear Momentum = > Linear Velocity of Cavitation Bubble
Reversal of Linear Momentum = > Linear Velocity of Cavitation Bubble + Linear Velocity of Retreating Popper
Termination of Rotational Momentum = > Linear Velocity of Cavitation Bubble + Angular Velocity of Cavitation Bubble
Reversal of Rotational Momentum = > Linear Velocity of Cavitation Bubble + Angular Velocity of Cavitation Bubble + Linear Velocity of Retreating Popper + Angular Velocity of Retreating Popper

Imagine if there are two spheres in water, if you pull them apart water will rush in between them. If fast enough, water can rush in fast enough and the liquid water will turn into water vapor. This is what happen if propellers in water spin too fast. If you only pull on one sphere the volume in between expands slower than if both moved. Now if you not only pull them apart, but you also increase their size and spin them, even more space develops between them as well as vorticity. This is what happens when a loop in the whip terminates, the inertial fluid drag pocket is now a torus (donut shaped) that is spinning. The torus is the motion envelope of the inertial fluid drag pocket and not just the pocket itself. Also the spinning action will cause a centrifugal reaction assisting the toroidal cavitaion bubble to increase in size. Imagine the air/water around it on a merry-go-round wanting to continue motion outward.

I hope this helps explain what happens when a whip cracks!

My basis: A Master's Degree in Multi-Phase Interaction in Computational Fluid Dynamics; Programmer for Institute of Hydraulic Research, Research with Eglin Air Force Base in High Speed Fluid Dynamics; Speaker at an American Institute of Aeronautics and Astronautics Conference on Multi-Phase, Multi-Scale, and Multi-Material Flow; and Discussion with Japanese Universities on Shockwave Production and Numerical Simulation of Shockwaves.

P.S. I have debated finding a University to acquire my Ph. D. in Fluid Dynamics with my dissertation on Whip Cracking Shock Wave Dynamics.