Common underlying physics of propulsion from kayaks to jets

[Asimov]

I had trouble titleing this topic and hope this is the right section. It might drift into many interesting side topics.Of itself it isnt profound. Surely not religion.

 

A jet fighter's nozzel is large at first giving a larger slower moving column of air to move the slowly accelerating jet. The nozzle is at it's narrowest column and the gases at the higest velocity at high speeds.Why? This is similar to kayak racing. To accelerate rapidly for short sprints one uses a large paddle blade but it is too tiresome to maintain long.The velocity is directly proportional to the stroke rate. A smaller blade allows one to maintain the high stroke rate much longer. Once finished accelerating you go about the same speed with either paddle at a given rate.Think of the blade as anchored in water as the boat moves forward.The more splash or noise with the blade the less efficient.You may even exceed the hull speed a little with a very sharp piercing bow and a rapid efficient cadence

 

Bicycle racers learn to "spin" at 90-100 or so strokes to maintain speeds for long periods.As long as you dont spin out where you are bouncing up and down you cover longer distances faster. You can go as fast spinning 1/2 as much with twice as big a gear but must push twice as hard and will not go far. Cars are similar , lower gearing to higher gearing as the speed goes up.The differenc being they have much more horse power to play with.Why does a human runner accelrate faster from a standing start than a horse or bicylist?

 

Not real profound but food for thought.

[Casey Wood]

Hi Asimov,

 

I think I can take the first question regarding jets. This is due to the law of conservation of momementum (really just a sub-law of the law of conservation of energy). The flow at the at the beginning of the nozzle must be equal to the flow out of the nozzle. We can define flow as Q=Av, where A is area, and v is velocity. For the momentum to be conserved Qin must equal Qout. We can state conservation of momentum by taking a unit Volume and therefore by letting density equal mass we have: dav_in - dav_out = 0. Where d is density (usually denoted by the greek letter rho). Because the surface area of the nozzle has decreased, the velocity of the expelled gases must increase to conserve momentum. As that velocity increases, the jet gets more thrust and must accelerate forward according to Newton's Third Law. The jet will remain at constant velocity when the sum of the forces acting perpendicular to its motion are equal to its thrust (assuming that it is flying at constant altitude).

 

In fact, as I read your questions again, I'm thinking that all of these ideas come down to the conservation of energy. Yet, I focus mostly on fluid dynamics, so I'll let some other folks go after the remaining questions. This is a fun post. If you would like me to bring in some more advanced mathematics or derivations let me know. Fun Stuff!

[Asimov]

Howdy Casey and thanx. I follow and it is about conserving energy.My son is an expert on that! As the turbine spins the out flow should equal the inflow of air I follow, but when the fuel is injected and there is combustion then the exhaust flow would be much more than inflow.Additional gases. Correct? In a ramjet at very high speeds the inflow is compressed without turbines explodes and goes aft. Variable pitch props do much the same thing as the variable nozzles.

[Casey Wood]

Hi Asimov,

 

It appears that we are talking about two different points in our control volume. So, let the system for flow-in be defined exactly in the front of the cowl, and flow-out at the exterior of the nozzle. We can simplify our system in that fashion. Introducing heat in the system due to combustion can then be taken as nominal. True, combustion increases the velocities of the compressible fluids moving through the control volume; by adding fuel, we have also added mass, which means that our densities inside the control volume have increased. If there has been an increase in density inside the control volume, then velocity must increase at the entrance to the control volume; remembering that the area-in, and ambient air densities remain constant. So, the flow-in is Qin and it is equal to Qout. If I increase Qout, then Qin increases. By adding the jet fuel inside the control volume, I have increased Qout, and I can suck more air into the jet, thereby increasing the velocity of the fluid moving through the control volume.

 

These concepts are not intuitive and they are difficult to understand. I have often argued that fluid mechanics is the third realm of modern physics, relative to quantum mechanics and general relativity. Do not be discouraged if they don't come to you as easily as GR and QM. If my explanation has not been satisfactory, then I am happy to take any more questions you may have on this subject.

Edited September 2, 2015 by Casey Wood

[Asimov]

Thanks, makes total sense though not what I expected. You explained it well.

[OptimisticCynic]

Human versus equine: proportion of available pushing force to mass is greater for the human. fH/mH > fE/mE

 

Runner versus bicyclist: on the common style bicycle it is very difficult for the rider to apply more force to the pedal than his mass being pulled down by gravity (his weight) whereas the runner is able to push himself forward with a force well in excess of his weight. On a recumbent style cycle, with the proper gearing, the rider may be able to apply more force to moving forward than the runner who also has to continue to lift himself while accelerating forward. But most likely the wheels would slip and the runner would pull ahead.