Calculating propeller shakes using a guessing stick

Many many years ago, before we had electronic calculators and computers were as big as garden sheds, I studied to be an engineer.  To do our sums we used slide rules, or guessing sticks as some of our more traditionally minded lecturers described them.  In those days if you asked an engineer to multiply 3 times 2 he would fiddle with his slide rule for a minute and then pronounce that the answer was about 5.95. I still have my slide rule in it’s original cardboard box and I couldn’t bear to part with it although I haven’t used it for years.  Nor have I used any of my engineering education, because I left engineering to pursue things I was better at. However for one day only I am trying to be an engineer again.

I was musing on Herbie’s propeller that has picked up a ding at sometime, probably by a blade striking a shopping trolley or something similar.  Feeling round the edge of the blades, one of them has a depression or flat spot on the edge, and this may have something to do with the fact that the transmission doesn’t run as smoothly as it used to.  So it occurred to me that I might be able to do a sum to get an idea of how much this little ding might be unbalancing the prop.  Looking at the little brass weights we have on our kitchen scales I reckon that the ding may have removed or displaced about five grams of bronze.  Does that make much difference?  Well I cast my mind back to a centrifugal force formula. How much centrifugal force is exerted by a 5 gram weight whirling round at 700 rpm (half engine speed at our normal cruising revs – half because the gearbox reduces at two to one)  at a radius of 8.5 inches. Luckily we old 1960 and 1970s engineers were trained to work in both metric and imperial measures so mixing grams and inches is something we can cope with. The formula is mass times radius times the square of the rotational speed (measured in radians per second).  I actually remembered that after 40 years!!!

OK so applying the formula, our little five gram chip of bronze whizzing round at 750 rpm turns out to exert an imbalance force of six and a half newtons, that’s over two thirds of a kilogram or about pound and a half in old money!  I read somewhere recently that propeller manufacturers only reckon on a five year life for props. Cavitation, dings and bends, and granular separation of the copper and tin that make up the bronze all take their toll. Next time Herbie comes out of the water, I’ll get a new prop fitted. It’s only money.

PS have I got this right Rick? (Rick is a proper engineer and will probably tell me there is more to it than just centrifugal force).