Help with a swmming math problem

Maths first. Grammars second. Oh, silly Jim. Syd is using British english. They do maths and go to hospital, instead of doing math and going to a hospital. And don't get me started on chips (french fries), crisps (potato chips), biscuits (cookies), etc.

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.

Effort level should be calculated off heart rate not time. 100% effort for me is 12 x 100's on 1:20. 90% is on 1:25 and 75% is 1:30. At 1:20 I have a heart rate in the mid to upper 150's. at 1:30 it is in the low 120's.

Effort level should be calculated off heart rate not time. 100% effort for me is 12 x 100's on 1:20. 90% is on 1:25 and 75% is 1:30. At 1:20 I have a heart rate in the mid to upper 150's. at 1:30 it is in the low 120's. The more I think about this, the more I think it is a bad idea. If you max heart rate is 200 bpm, and that is your 100% marker, then a 95% effort if 190 bpm, right? So you maintain the same heart rate for a 50 or a 1500? I don't think that makes sense.

The more I think about this, the more I think it is a bad idea. If you max heart rate is 200 bpm, and that is your 100% marker, then a 95% effort if 190 bpm, right? So you maintain the same heart rate for a 50 or a 1500? I don't think that makes sense. I should have been more specific: I was suggesting training off max aerobic heart rate, not max heart rate. That is why I gave the example set.

I was also taught that gas is actually petrol, colour is spelled with a 'u', the trunk of a car is a 'boot' and the hood a 'bonnet'. I went to a British school in my teens when I lived overseas, and was forced to use spellings like colour and defence. While I was happy to study ALL maths, not just the one, I have to admit that their tendency to refer to erasers as "rubbers" was a little confusing to me in these formative years. ("You want to borrow my WHAT? And why would you think I would want it back?") :bolt:

He brought his maths home. Maths is his favorite subject. His maths is improving. He buys his maths supplies from the local maths supply warehouse, Maths Is Us. A rival chain, Maths R Us, was so roundly ridiculed by Europeans that it had no choice but to shut down. The former manager is in hospital. I used to have a head for maths, but of late maths is flying out my ears. Wait, that is impossible. Maths is flying out one of my ears. If a maths is cut in half and each piece regenerates, are you left with two mathses? And so wiles away the waning hours of a long day spent looking at the maths in my checkbook. Given the negative numbers featured therein, the plural implications of "maths" seem particular cruel to me now. But perhaps I am being overly sensitive. Perhaps some warm milk and a biscuit and bed, that's the ticket. Ha! Ha! Very funny, Jim. Where I learnt my English, the subject is called Mathematics (One would think 'maths' would be the obvious short form, but apparently not). Indeed, the North American rendering of Math has always seemed strange to us. (But in deference to you all, you will notice I included 'math' in the thread title). I somehow slipped up when writing the thread. Apologies! I was also taught that gas is actually petrol, colour is spelled with a 'u', the trunk of a car is a 'boot' and the hood a 'bonnet'. My teacher did say, however, that to refer to someone as 'a FRUIT CAKE', has nothing to do with their propensity for eating the stuff. ..the plural implications of "maths" seem particular cruel to me nowYou're particular funny! :bolt: fondly, Syd

the problem with your math is each 25 would take 1/3 of your 100's time so if you expand that out to 100 isn't it 4 x 1/3 = 4/3 or 133 1/3% which is 33% more time wise if you go 1:00 in the 100 free wouldn't 75% effort or 25% slower be 1:15 The obvious corollary here is that it is impossible for any two people to agree on what 75% effort actually means. I don't use % efforts in my workouts, but if I did, I'd use the definition I provided, because it is so simple, it can be applied even when the maths-challengeds are too tireds to calculates diddlys/squats.

Thanks for the review. I do not think there is a mistake when I expand out the terms: P_swim = ((C_flow * V^2) * D_pool) * t_interval keeping in mind V = D_pool / t_interval let us now substitute terms for V P_swim = ((C_flow * (D_pool/t_interval)^2) * D_pool) * t_interval one of the t_interval's gets canceled out.

Great topic for discussion Perhaps we should consider the two separate issues: - Physiological response to exercise stress (i.e. heart rate, repirotory rate, lactic acid build up etc.) - Power resistance "curve" provided by swimming activity The power resistance "curve" for swimming activity would be where you could find the answer to the original question of a 3/4 pace swim to simulate competition effort. Hydrodyanamic drag of a swimmer body through the water increases as the velocity squared. As a result, the power required to make a interval time will increase as the square of the relative change in time. Consider the following equations F_drag = C_flow * V^2 V_swim = d_swim/t_interval W_swim = F_drag * D_pool P_swim = W_swim * t_intervalwhere: F_drag - hydrodyamic drag of swimmer body through water V_swim - swimmer velocity through water d_swim - pool distance swum t_interval - competition time or training pace interval W_swim - work expenditure of swimmer. This quantity is directly related to required caloric intake to recover from swim workout P_swim - power expenditure of swimmer. This quantity is related to swimmer bodies capability to convert chemical energy stores into usefull muscular power output I put in the term C_flow as a constant that would represent an individuals flow resistance in the water. It considers skin friction, form drag and stroke efficiency. You would determine your personal C_flow number from swim tests. You might have one C_flow for sloppy swimming and one for high quality ;) If you take all these equations and combine you could get the following: P_race = C_flow * (d_swim^2 / t_race) So if you consider C_flow and d_swim the same between train and race conditions and wanted an interval that was three quarter (75%) of your race speed power output you would just have. t_train = t_race/0.75 You were correct in your original answer. For me the challenge that engages me in those long sets of training intervals is working toward keeping efficiency high (make C_flow low) for strokes and turns and to simulate short periods of race conditions in training to monitor any changes in C_flow. Happy swimming. I believe there is a mistake in your math such that P_race should = C_flow * (d_swim^2 / t_race^2).