I am trying to work out the mathematics behind the design of an old mechanical brake tester. The device sits in the passenger foot well of a vehicle and tests the brake efficiency. The device is basically a pendulum with a stylus attached, and as the brakes are applied the pendulum swings and draws up a card. The card is marked in acceleration, or deceleration in this case, (as a % of local gravity) in increments of 10 up to 100% (9.81 m/s2).
I am trying to verify the mathematics behind how the instrument functions, by applying an angle to the device, essentially simulating an acceleration. When testing the equipment I can raise the stylus ever so slightly off the paper to remove the effects of friction, so applying an angle will result in a true acceleration reading.
I equated this to; Acceleration = g sin (34) Then I would need to rearrange this to calculate which angles I need to be applying to test each nominal acceleration reading (10,20 and so on).
Is friction a large enough factor that the card will be accounting for this? The distance between the scale divisions on the card get smaller and smaller as it progresses towards 100%. Should I be correcting for the initial friction coefficient. I have the measurements for the length of the pendulum 0.140m and the weight on the end of the pendulum 10 oz.
I found a similar thread of discussion but the results I am obtaining in my tests are slightly out from my calculations. However this error could be in the device itself.