[hpv-boats] converting pedal power to prop power right angles dennis

[Rick Willoughby]

Dennis
The torque on the crank varies approximately sinusoidally because the  
model assumes the leg force is constant.  The sinusoid shape results  
from the effective lever length of the crank varying from zero at the  
dead spot up to the full crank length at the maximum torque.  This  
applied torque is the red trace that I call "leg drive" - it is  
mislabelled (N); it should be(Nm), being the crank torque.  Note that  
I do not force the sinusoidal motion - the shape of the curve is the  
result of the constant leg force and the effective lever length of  
the crank.  So the more the crank speed varies the more the shape of  
the curve departs from a true sinusoidal shape.

If there was no compliance in the shaft then the thrust curve would  
be a similar sinusoidal curve to the crank torque and it would be in  
phase.  The crank speed would be almost a straight line with a small  
amplitude sinusoidal wave impressed in phase with the crank.  When  
the shaft has compliance there is a lag between the crank torque and  
the thrust.

At the dead spot the shaft is completely unwound, or even wound in  
reverse due to the boat driving the crank.  After the deadspot the  
increasing torque, with little resistance from the shaft due toits   
unwound state, enables high crank speed to the point where the shaft  
gets wound up and starts accelerating the boat and slowing the crank  
speed.  In the curve you refer to the average crank speed is 71rpm  
but it overshoots to about 82rpm.  The slowing from 82rpm back to  
71rpm causes an increase in boat speed over the average.

There is an exchange of energy between the shaft spring energy and  
the boat momentum.  The frequency of this is a function of the boat  
mass and the shaft spring constant.  The more compliant the shaft  
then the greater the amount of energy transfer between shaft and boat  
momentum.  In fact if you look at the second chart I linked to with  
the very compliant shaft then you can see there is some variation in  
the boat speed:
http://www.rickwill.bigpondhosting.com/Boat_Shaft_1to4%20_flex.pdf
This is similar to the sort of speed variation that you would see in  
a rowing shell that has momentum transfer from body to boat and  
thrust variation due to the stroking of the oars.

If you replaced your steel shaft with an aluminium shaft of same  
diameter you will have enough compliance to reduce your biomechanical  
efficiency and the dynamics will be more apparent.  A good shaft will  
have similar feel to a bike on the road i.e. very well connected  
rather than rubbery.

Rick



Hi Rick
On your dynamic model of crank drive for the V14 hull with 1.4 gear  
ratio:-
The thrust curve has a major dip just after the peak, what causes  
this as
there is not a similar dip in the leg drive.

Dennis

Rick Willoughby
rickwill at bigpond.net.au
03 9796 2415
0419 104 821