High School Maximum Force on transom of a boat under acceleration

[ggcarmichael]

I'm trying to calculate the maximum Force in PSI applied to the transom of a planing boat under acceleration using F=ma.

boat mass is 300kg
accelerates from 0 to 10m/s in 6 seconds
F=ma -> 500N = 300kg *(10m/s/6s) = 112.4045lbf
the contact area between the boat transom and motor is 1000 mm2 = 1.55in2

112.4045lbf/1.55in2=72.51903226 lbs/in2 (PSI)

If my method of solving is correct, is 72.51903226 lbs/in2 (PSI) the maximum force applied and is this the force that is applied at t0?

thank you,
Gil

 

[hutchphd]

Two things:
Please use one set of units, preferably MKS (SI) and convert at the end if you wish.
While accelerating the motor also has to overcome drag forces which are quite variable on a planing hull

So long as the propeller does not cavitate, the acceleration over the first second will give a better measure of the force (the drag will be less at low speed). Why do you want the pressure and not the force? How important is the accuracy of the number?

 

[ggcarmichael]

I thought I was using SI for the bulk of the equation and converting at the end but I wasn't sure I was doing it correctly.
I'm want to use PSI because I want to test the solution using a hydraulic press to experiment with different transom thicknesses in plywood.

 

[jack action]

What you have calculated is the average acceleration. It may (and probably) be higher at the beginning of the acceleration period, and slowly decreasing as speed increases. But every other scenario is also possible (for example, acceleration increasing as speed increases).

The correct way to design this safely would be to evaluate the maximum force the motor/propeller combination can produce and go with that. Then your transom would be designed for a particular powertrain, not for a particular performance of the boat.

Don't forget that in addition to a horizontal force, the propeller will also create a twisting moment on your transom.

 

[hutchphd]

If the limiting factor is pressure then a steel plate to spread the force may make the most sense. And assuming a uniform acceleration will underestimate peak force. Put in a lot of margin. Also wet plywood loses compression strength spectacularly and can fail suddenly.

 

[Lnewqban]

The propeller may be stalling at the lowest velocity of the boat and its thrust should increase as that velocity increases.
Besides, there is more water drag as the boat gets closer to reaching the maximum velocity you mention.

That force that you have calculated is probably about half the maximum pushing force of the propeller, which is trying to move underneath the boat and trying to twist the transom backwards.

 

[jrmichler]

Two things to keep in mind:

1) The propeller is pushing down "there", while the motor is mounted up "here". It's prying on the transom, so there is a bending force on the transom. That bending force is more correctly called a moment.

2) The real design condition for a transom with an outboard motor is when moving at speed, the motor hits a tree stump or other underwater object, gets bounced up into the air, and slams down. Those forces are much higher than any normal running forces, and very difficult to calculate. Which is why boat transoms are designed by experience - copying the design of transoms that have survived similar abuse.