Sawtooth coast tests

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   Further to the 'measuring power input' thread, I dug up some of my coasting data to see how much noise there was in the data.
I've long had a theory that I coast better when the pedals are horizontal than when they're vertical, so I used the computer to put this to the test.
My computer has a 'pacer' feature where it makes a sound whenever you exceed a certain speed. I did my coasting tests by accelerating up to this speed, coasting for a few metres then accelerating up to the target speed again. This way you can collect a lot of data very quickly for a specific speed, and it should also be ideal for testing accessories e.g. what's the advantage of a given tailbox, or the cost of putting a flag on your trike. A further advantage is that you don't need much space to do a sawtooth coast test - whereas to do a coast from 40->10mph you'd almost need a runway.
Computers willing, there should be a graph below, that shows the data from my sawtooth coasts (I've been calling them that for obvious reasons - has anybody ever come up with a different name for them?). The first step in the analysis is to select the region of data you're interested in, and set the maximum and minimum speeds (a). The next step is to find periods of deacceleration within the limits (b) - marked red. The final step is to plot these against a graph (c - blue curvy lines), remove outliers (times when I'd obviously had to hit the brakes - or started pedalling too early), and fit a line of best fit (linear, not polynomial - red lines) to each. 
Fitting a linear fit to an exponential function will obviously result in some bias. I haven't yet worked out how large that bias is likely to be. I also don't like removing outliers by eye. The brain is very subtle, and even with the best of scientific intentions, it would be all too easy to introduce bias at this stage. I think this process should be automated in the future.
The power is calculated from the gradient of the line and the equation E=0.5MV^2. I know this could be improved by adding a term for the energy stored in the wheels. I also guessed at the weight - I'm pretty sure this is likely to be more accurate than trusting my bathroom scales.
I did my first set of tests in some local tennis courts that were laser-levelled and have a very smooth surface. The area was 1 court long by 3 courts wide. It was windless, very cold (1 degree C) and the ground was dry.
Results

In my first test, I measured the power required to maintain 5.77 Meters/Second maintain (20.79 Km/hr). In this run, I obtained 27 valid results for the vertical cranks condition with a mean of 139.5 watts and a standard deviation of 6%. For the horizontal crank condition, I obtained 16 valid measurements and the mean was 139.9 watts with a standard deviation of 6.5%. A 1-way Anova of the first 16 results from the vertical crank condition and the results from the horizontal crank condition found no significant difference.
On another day, I ran an identical test that was analysed at 5.5 M/S (19.8Km/hr). Coasting with the cranks horizontal required 151.8 watts; coasting with the cranks vertical required 152.1 watts. The standard deviations were 7.1 and 8.1% respectively. The data were compared using 1-way Anova, and were not found to differ  significantly from one another (p = 0.96).
Due to limitations of space, it was impractical to cycle at speeds in excess of 6M/S in the tennis courts so I found a circuit that appeared almost flat and was fairly straight. I tested both conditions a third time at 8.45 M/S (30.42 Km/hr). For both conditions, I obtained 8 valid measurements. The power required was 350.6 W for the vertical cranks condition, and 331 W for the horizontal cranks condition. The standard deviations were 13.2% and 15.6% respectively. The difference was significant at the 95% level (p = 0.044).
In a final test, I repeated the 6M/S pacer tests on this new course, analysing them at a speed of 5.5 M/S. I obtained 20 valid results for the vertical cranks condition and 7 valid results for the horizontal cranks condition. As for other tests at this speed, no significant differences were found between the vertical and horizontal crank conditions (means = 148.3; 149.1; standard deviations = 12.5% and 17.3% respectively).
I haven't researched the best type of statistical power calculation to do, but doing an ANOVA of 16 measurements for vertical-crank coasting versus the same measurements x 0.95 gave a p value of 0.035 which is significant. I'm sure the statisticians would throw their hands up in horror at this method, but it seems likely that pretty feasible numbers of measurements are sufficient to detect a power difference as small as a few percent.
Discussion
The power values I got were higher than expected. I don't completely disbelieve them as it was cold; my bike has lots of mudguards etc. and I was wearing a puffy coat and jeans... But I'm still left wondering if I haven't got a rogue constant in my code somewhere. This affects the validity of the results, but not the variability, which is what I'm interested in here.
The differences in power values at 5.5M/S don't particularly worry me - they were on different surfaces.
I did get a significant result that confirmed my hypothesis re. vertical v. horizontal cranks - at high speed. But I would need to repeat the measurements on a better track before I believed it. Especially as I found no difference whatsoever at the lower speeds for which I have much more data, and that were obtained on a better surface. 
Steering movements could cause the pacer to sound, go silent then sound again. I assume this means that energy is being stored and released during steering, and that this could account for some of the variation in the data. In my tennis court tests I had to brake and turn on every leg of the test, and this made it difficult to avoid steering movements 
The variability in my data was smaller on the smooth tennis courts than for the other circuit, that as far as I could perceive was slightly cambered but had no perceptible gradient (in the direction of motion).
It's much easier to accelerate accurately to the correct speed and maintain a straight line, if you're not having to turn and brake frequently. I'm optimistic that it would be possible to get more consistent data than those I've reported here, given a good test track. Even so, I think the method is capable of giving meaningful results and finding significant differences. I guess it depends on your definition of a significant difference.
As discussed, this is all preliminary. I simply don't have time to do any more data collection and analysis at the minute, and I shall continue to be busy for the forseeable future. I'll lend people my prototype computers if they're interested.
Kit

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kit wolf Members Profile Send Private Message Find Members Posts Add to Buddy List Visitor (regular) Joined: 23 March 2005 Status: Offline Points: 220	Topic: Sawtooth coast tests Posted: 07 March 2006 at 6:06pm
	Further to the 'measuring power input' thread, I dug up some of my coasting data to see how much noise there was in the data. I've long had a theory that I coast better when the pedals are horizontal than when they're vertical, so I used the computer to put this to the test. My computer has a 'pacer' feature where it makes a sound whenever you exceed a certain speed. I did my coasting tests by accelerating up to this speed, coasting for a few metres then accelerating up to the target speed again. This way you can collect a lot of data very quickly for a specific speed, and it should also be ideal for testing accessories e.g. what's the advantage of a given tailbox, or the cost of putting a flag on your trike. A further advantage is that you don't need much space to do a sawtooth coast test - whereas to do a coast from 40->10mph you'd almost need a runway. Computers willing, there should be a graph below, that shows the data from my sawtooth coasts (I've been calling them that for obvious reasons - has anybody ever come up with a different name for them?). The first step in the analysis is to select the region of data you're interested in, and set the maximum and minimum speeds (a). The next step is to find periods of deacceleration within the limits (b) - marked red. The final step is to plot these against a graph (c - blue curvy lines), remove outliers (times when I'd obviously had to hit the brakes - or started pedalling too early), and fit a line of best fit (linear, not polynomial - red lines) to each. Fitting a linear fit to an exponential function will obviously result in some bias. I haven't yet worked out how large that bias is likely to be. I also don't like removing outliers by eye. The brain is very subtle, and even with the best of scientific intentions, it would be all too easy to introduce bias at this stage. I think this process should be automated in the future. The power is calculated from the gradient of the line and the equation E=0.5MV^2. I know this could be improved by adding a term for the energy stored in the wheels. I also guessed at the weight - I'm pretty sure this is likely to be more accurate than trusting my bathroom scales. I did my first set of tests in some local tennis courts that were laser-levelled and have a very smooth surface. The area was 1 court long by 3 courts wide. It was windless, very cold (1 degree C) and the ground was dry. Results In my first test, I measured the power required to maintain 5.77 Meters/Second maintain (20.79 Km/hr). In this run, I obtained 27 valid results for the vertical cranks condition with a mean of 139.5 watts and a standard deviation of 6%. For the horizontal crank condition, I obtained 16 valid measurements and the mean was 139.9 watts with a standard deviation of 6.5%. A 1-way Anova of the first 16 results from the vertical crank condition and the results from the horizontal crank condition found no significant difference. On another day, I ran an identical test that was analysed at 5.5 M/S (19.8Km/hr). Coasting with the cranks horizontal required 151.8 watts; coasting with the cranks vertical required 152.1 watts. The standard deviations were 7.1 and 8.1% respectively. The data were compared using 1-way Anova, and were not found to differ significantly from one another (p = 0.96). Due to limitations of space, it was impractical to cycle at speeds in excess of 6M/S in the tennis courts so I found a circuit that appeared almost flat and was fairly straight. I tested both conditions a third time at 8.45 M/S (30.42 Km/hr). For both conditions, I obtained 8 valid measurements. The power required was 350.6 W for the vertical cranks condition, and 331 W for the horizontal cranks condition. The standard deviations were 13.2% and 15.6% respectively. The difference was significant at the 95% level (p = 0.044). In a final test, I repeated the 6M/S pacer tests on this new course, analysing them at a speed of 5.5 M/S. I obtained 20 valid results for the vertical cranks condition and 7 valid results for the horizontal cranks condition. As for other tests at this speed, no significant differences were found between the vertical and horizontal crank conditions (means = 148.3; 149.1; standard deviations = 12.5% and 17.3% respectively). I haven't researched the best type of statistical power calculation to do, but doing an ANOVA of 16 measurements for vertical-crank coasting versus the same measurements x 0.95 gave a p value of 0.035 which is significant. I'm sure the statisticians would throw their hands up in horror at this method, but it seems likely that pretty feasible numbers of measurements are sufficient to detect a power difference as small as a few percent. Discussion The power values I got were higher than expected. I don't completely disbelieve them as it was cold; my bike has lots of mudguards etc. and I was wearing a puffy coat and jeans... But I'm still left wondering if I haven't got a rogue constant in my code somewhere. This affects the validity of the results, but not the variability, which is what I'm interested in here. The differences in power values at 5.5M/S don't particularly worry me - they were on different surfaces. I did get a significant result that confirmed my hypothesis re. vertical v. horizontal cranks - at high speed. But I would need to repeat the measurements on a better track before I believed it. Especially as I found no difference whatsoever at the lower speeds for which I have much more data, and that were obtained on a better surface. Steering movements could cause the pacer to sound, go silent then sound again. I assume this means that energy is being stored and released during steering, and that this could account for some of the variation in the data. In my tennis court tests I had to brake and turn on every leg of the test, and this made it difficult to avoid steering movements The variability in my data was smaller on the smooth tennis courts than for the other circuit, that as far as I could perceive was slightly cambered but had no perceptible gradient (in the direction of motion). It's much easier to accelerate accurately to the correct speed and maintain a straight line, if you're not having to turn and brake frequently. I'm optimistic that it would be possible to get more consistent data than those I've reported here, given a good test track. Even so, I think the method is capable of giving meaningful results and finding significant differences. I guess it depends on your definition of a significant difference. As discussed, this is all preliminary. I simply don't have time to do any more data collection and analysis at the minute, and I shall continue to be busy for the forseeable future. I'll lend people my prototype computers if they're interested. Kit

kit wolf Members Profile Send Private Message Find Members Posts Add to Buddy List Visitor (regular) Joined: 23 March 2005 Status: Offline Points: 220	Posted: 07 March 2006 at 7:25pm
	Text from the above, in a readable format... 'pedals' should read 'cranks' - corrected. Further to the 'measuring power input' thread, I dug up some of my coasting data to see how much noise there was in the data. I've long had a theory that I coast better when the cranks are horizontal than when they're vertical, so I used the computer to put this to the test. My computer has a 'pacer' feature where it makes a sound whenever you exceed a certain speed. I did my coasting tests by accelerating up to this speed, coasting for a few metres then accelerating up to the target speed again. This way you can collect a lot of data very quickly for a specific speed, and it should also be ideal for testing accessories e.g. what's the advantage of a given tailbox, or the cost of putting a flag on your trike. A further advantage is that you don't need much space to do a sawtooth coast test - whereas to do a coast from 40->10mph you'd almost need a runway. Computers willing, there should be a graph below, that shows the data from my sawtooth coasts (I've been calling them that for obvious reasons - has anybody ever come up with a different name for them?). The first step in the analysis is to select the region of data you're interested in, and set the maximum and minimum speeds (a). The next step is to find periods of deacceleration within the limits (b) - marked red. The final step is to plot these against a graph (c - blue curvy lines), remove outliers (times when I'd obviously had to hit the brakes - or started pedalling too early), and fit a line of best fit (linear, not polynomial - red lines) to each. Fitting a linear fit to an exponential function will obviously result in some bias. I haven't yet worked out how large that bias is likely to be. I also don't like removing outliers by eye. The brain is very subtle, and even with the best of scientific intentions, it would be all too easy to introduce bias at this stage. I think this process should be automated in the future. The power is calculated from the gradient of the line and the equation E=0.5MV^2. I know this could be improved by adding a term for the energy stored in the wheels. I also guessed at the weight - I'm pretty sure this is likely to be more accurate than trusting my bathroom scales. I did my first set of tests in some local tennis courts that were laser-levelled and have a very smooth surface. The area was 1 court long by 3 courts wide. It was windless, very cold (1 degree C) and the ground was dry. Results In my first test, I measured the power required to maintain 5.77 Meters/Second maintain (20.79 Km/hr). In this run, I obtained 27 valid results for the vertical cranks condition with a mean of 139.5 watts and a standard deviation of 6%. For the horizontal crank condition, I obtained 16 valid measurements and the mean was 139.9 watts with a standard deviation of 6.5%. A 1-way Anova of the first 16 results from the vertical crank condition and the results from the horizontal crank condition found no significant difference. On another day, I ran an identical test that was analysed at 5.5 M/S (19.8Km/hr). Coasting with the cranks horizontal required 151.8 watts; coasting with the cranks vertical required 152.1 watts. The standard deviations were 7.1 and 8.1% respectively. The data were compared using 1-way Anova, and were not found to differ significantly from one another (p = 0.96). Due to limitations of space, it was impractical to cycle at speeds in excess of 6M/S in the tennis courts so I found a circuit that appeared almost flat and was fairly straight. I tested both conditions a third time at 8.45 M/S (30.42 Km/hr). For both conditions, I obtained 8 valid measurements. The power required was 350.6 W for the vertical cranks condition, and 331 W for the horizontal cranks condition. The standard deviations were 13.2% and 15.6% respectively. The difference was significant at the 95% level (p = 0.044). In a final test, I repeated the 6M/S pacer tests on this new course, analysing them at a speed of 5.5 M/S. I obtained 20 valid results for the vertical cranks condition and 7 valid results for the horizontal cranks condition. As for other tests at this speed, no significant differences were found between the vertical and horizontal crank conditions (means = 148.3; 149.1; standard deviations = 12.5% and 17.3% respectively). I haven't researched the best type of statistical power calculation to do, but doing an ANOVA of 16 measurements for vertical-crank coasting versus the same measurements x 0.95 gave a p value of 0.035 which is significant. I'm sure the statisticians would throw their hands up in horror at this method, but it seems likely that pretty feasible numbers of measurements are sufficient to detect a power difference as small as a few percent. Discussion The power values I got were higher than expected. I don't completely disbelieve them as it was cold; my bike has lots of mudguards etc. and I was wearing a puffy coat and jeans... But I'm still left wondering if I haven't got a rogue constant in my code somewhere. This affects the validity of the results, but not the variability, which is what I'm interested in here. The differences in power values at 5.5M/S don't particularly worry me - they were on different surfaces. I did get a significant result that confirmed my hypothesis re. vertical v. horizontal cranks - at high speed. But I would need to repeat the measurements on a better track before I believed it. Especially as I found no difference whatsoever at the lower speeds for which I have much more data, and that were obtained on a better surface. Steering movements could cause the pacer to sound, go silent then sound again. I assume this means that energy is being stored and released during steering, and that this could account for some of the variation in the data. In my tennis court tests I had to brake and turn on every leg of the test, and this made it difficult to avoid steering movements The variability in my data was smaller on the smooth tennis courts than for the other circuit, that as far as I could perceive was slightly cambered but had no perceptible gradient (in the direction of motion). It's much easier to accelerate accurately to the correct speed and maintain a straight line, if you're not having to turn and brake frequently. I'm optimistic that it would be possible to get more consistent data than those I've reported here, given a good test track. Even so, I think the method is capable of giving meaningful results and finding significant differences. I guess it depends on your definition of a significant difference. As discussed, this is all preliminary. I simply don't have time to do any more data collection and analysis at the minute, and I shall continue to be busy for the forseeable future. I'll lend people my prototype computers if they're interested. Kit

Mr Blue Sky Members Profile Send Private Message Find Members Posts Add to Buddy List Visitor (regular) Joined: 15 March 2005 Location: United Kingdom Status: Offline Points: 103	Posted: 08 March 2006 at 12:00pm
	I like your "burn & coast" method: it sounds like it allows you to collect useful data much more quickly than coasting from say 20+ mph to 4 mph. Can't comment on your graphs because my computer wouldn't display them! I agree with you that the power values seem high: using your data for 5.77 m/s and 8.45 m/s suggests a rolling drag of around 10 N and a CdA of about 0.7 sq. m. What sort of bike did you use? As far as temperature is concerned, John Tetz's measurements suggest that there is a strong inverse relationship between RR and temp (his data appears on the MARS website). One thing you might consider worthy of investigation: the power increment of pedalling - could be tricky to measure, but I'm fairly sure that I can coast down some of my local hills faster than I can pedal down them! Good luck with your future measurements. Neil

kit wolf Members Profile Send Private Message Find Members Posts Add to Buddy List Visitor (regular) Joined: 23 March 2005 Status: Offline Points: 220	Posted: 08 March 2006 at 6:37pm
	In reply to queries: My bike is an M5 28/20 with underseat steering, a SON dynohub and lots of mudguards and pumps added to ruffle the airflow. No tailboxes or fairings. The stock version allegedly does 37.5kph at 250W if memory serves. But I'm not sure if that figure refers to the original 28/20 or to my newer version, which I always felt was appreciably slower. I've noticed the pedalling v. coasting effect too. It was part of my rationale for the first tests - I figured that if some crank positions produce more drag than others then this could account for the difference. Perhaps static tests wouldn't be sensitive enough to show this up. In which case you could test it either by pedalling too slowly to apply any power, or backpedalling that I assume would be aerodynamically equivalent to forwards-pedalling. I gather that not everyone can see the graph. I think it's a firewall problem, so I've tried to post it to a server outside of the university. Trying again... Kit