Mathematically, how do you work out 'three quarter pace"?
Let's say (for the sake of easy calculations) your best time for an event is 1 minute. In practice, you want to go three quarter pace. So a 100% effort will result in a time of 60 seconds. A 75% effort should result in a longer time. My rudimentary maths tells me I should divide 100 by 75 and multiply the result by 60. That works out to 80 seconds, which is a minute and 20 seconds. Why does that sound much slower than what I would normally envisage three quarter pace to be? Or is my maths completely messed up?
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Former Member
Great question.
Let’s assume that your 100% effort is your best time in that distance relatively recently, and you are similar in shape and size as when you swam that time. So we know distance is constant, the body in motion is constant and Newton did the hard work.
Work = Force * Change in displacement. Change in displacement is constant since we are displacing a swimmer a fixed distance. Solve for Force.
Force = mass * acceleration. The swimmers mass is constant, solve for acceleration.
Acceleration is where we stop, or we get into calculus that should give us the same answer anyway. Acceleration is measured in distance / time squared units. Since distance is constant, this gives us our slope for time which is what we are interested in.
So decreased effort results in an exponential increase in time.
This is the formula I propose to calculate effort, based on the pseudo math above.
(1/E)^2 * B = T
E = effort (85% = .85)
B = best time (seconds)
T = decreased effort time (seconds)
Based on a 1:00 best time.
95% 1:06
90% 1:14
85% 1:23
80% 1:34
75% 1:46
70% 2:02
Plugging in my freestyle times, 95% is about as fast as I can hit in practice, 85% I can do a lot of repeats (maybe all practice long), and 80% is pretty slow recovery.
Great question.
Let’s assume that your 100% effort is your best time in that distance relatively recently, and you are similar in shape and size as when you swam that time. So we know distance is constant, the body in motion is constant and Newton did the hard work.
Work = Force * Change in displacement. Change in displacement is constant since we are displacing a swimmer a fixed distance. Solve for Force.
Force = mass * acceleration. The swimmers mass is constant, solve for acceleration.
Acceleration is where we stop, or we get into calculus that should give us the same answer anyway. Acceleration is measured in distance / time squared units. Since distance is constant, this gives us our slope for time which is what we are interested in.
So decreased effort results in an exponential increase in time.
This is the formula I propose to calculate effort, based on the pseudo math above.
(1/E)^2 * B = T
E = effort (85% = .85)
B = best time (seconds)
T = decreased effort time (seconds)
Based on a 1:00 best time.
95% 1:06
90% 1:14
85% 1:23
80% 1:34
75% 1:46
70% 2:02
Plugging in my freestyle times, 95% is about as fast as I can hit in practice, 85% I can do a lot of repeats (maybe all practice long), and 80% is pretty slow recovery.
