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#41




GPS Units = Show road steepness?
Ralph Barone writes:
Radey Shouman wrote: Zen Cycle writes: On Sunday, March 10, 2019 at 6:35:02 PM UTC4, Roger Merriman wrote: Sir Ridesalot wrote: Talking about GPS units on another thread reminded me of something else I wondered if they do. Does a bicycle GPS unit show you the steepness of roads? There's an area that I frequently ride where on road has short but very steep hills, another road a mile or so east of it has much more gradual hills whilst a third road to the west of the first one is a major highway that can be ridden with a bicycle. What I'm wondering is this: if someone unfamiliar with the area got there and used a GPS unit to show those three roads, would the GPS unit show them the different gradients of the roads? Or is that another function that they'd need to download or otherwise install? Cheers Various mapping sites will show the gradient, and some GPS units will show the gradient, in the same way that it can give improbable maximum speeds they can also give improbable max gradients or sometimes on very short ramps not notice it, there is a nasty little ramp nr my folks place, which is the software flattens claiming 12% when itâ€™s a fair cruel 25/30% even more cruel this weekend with a 50mph headwind. It's probably an averaging issue  taking enough samples before and after the section so that it flattens the pitch. It's the same basic issue as the speedometer kerfluffle. Numerical differentiation amplifies noise. I would think it was the opposite. Numerical integration suppresses spikes. I would call that the converse. But turning altitude data, which is what is actually measured, into a gradient is differentiation.  
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#42




GPS Units = Show road steepness?
Radey Shouman wrote:
Zen Cycle writes: On Monday, March 11, 2019 at 3:28:58 PM UTC4, Radey Shouman wrote: Zen Cycle writes: On Sunday, March 10, 2019 at 6:35:02 PM UTC4, Roger Merriman wrote: Sir Ridesalot wrote: Talking about GPS units on another thread reminded me of something else I wondered if they do. Does a bicycle GPS unit show you the steepness of roads? There's an area that I frequently ride where on road has short but very steep hills, another road a mile or so east of it has much more gradual hills whilst a third road to the west of the first one is a major highway that can be ridden with a bicycle. What I'm wondering is this: if someone unfamiliar with the area got there and used a GPS unit to show those three roads, would the GPS unit show them the different gradients of the roads? Or is that another function that they'd need to download or otherwise install? Cheers Various mapping sites will show the gradient, and some GPS units will show the gradient, in the same way that it can give improbable maximum speeds they can also give improbable max gradients or sometimes on very short ramps not notice it, there is a nasty little ramp nr my folks place, which is the software flattens claiming 12% when itâ€™s a fair cruel 25/30% even more cruel this weekend with a 50mph headwind. It's probably an averaging issue  taking enough samples before and after the section so that it flattens the pitch. It's the same basic issue as the speedometer kerfluffle. Numerical differentiation amplifies noise. Interesting how you characterize it as 'noise'. For the speedometer the main source of noise is quantization error, resulting from reducing a continuous wheel position to an integer number of revolutions. For the 2d field of altitudes obtained from a map I suspect that the quantization of position, ie, the limited number of data points, perhaps at irregular places, is the main source of noise. How to turn topographical survey data into something that looks like a continuous function is a whole field of study  there are many ways to go wrong, and no one perfect way to do it right. In either case, errors that would be fairly small in altitude or distance become larger when differentiated to estimate speed or gradient. Ah... I see your point now. 
#43




GPS Units = Show road steepness?
Am 12.03.2019 um 13:38 schrieb Zen Cycle:
On Monday, March 11, 2019 at 9:13:08 PM UTC4, Ralph Barone wrote: Radey Shouman wrote: Zen Cycle writes: On Sunday, March 10, 2019 at 6:35:02 PM UTC4, Roger Merriman wrote: Various mapping sites will show the gradient, and some GPS units will show the gradient, in the same way that it can give improbable maximum speeds they can also give improbable max gradients or sometimes on very short ramps not notice it, there is a nasty little ramp nr my folks place, which is the software flattens claiming 12% when itâ€™s a fair cruel 25/30% even more cruel this weekend with a 50mph headwind. It's probably an averaging issue  taking enough samples before and after the section so that it flattens the pitch. It's the same basic issue as the speedometer kerfluffle. Numerical differentiation amplifies noise. I would think it was the opposite. Numerical integration suppresses spikes. That's why I made the comment about the definition of 'noise'. I don't think differentiation is appropriate in this case, especially since we're doing simple math (not even algebra, let alone calculus). I would not talk about Math, Algebra or Calculus in this context but simple engineering, combined with 'finite difference' rather than differentiation or 'finite sums' rather than integration. We have 2dpoints with errors (x1,e1), (x2,e2), ... (xn, en). Total distance is easily calculated as xnx1 with an error estimation of (1/2 en  e1 ), i.e. the error on a total distance is similar to the error of each individual sample: very good results on a very simple algorithm. Sadly, total distance is not so useful when you take a round trip. Length of a track section is still an OK calculation where you get an error estimation in the order of k * e when you split your total track into k sections. As long as the size of each section is significantly larger than the typical error, the final result "trip distance" (and compared to this, 'average speed') is of sufficiently high quality. "Current speed" calculations (what you call 'differentiation') is extremely error prone: (x2  x1) / (t2  t1) gives you an error in the order of (e2+e1) / (t2t1). You interpolate the current speed by a measuring interval, and splitting the sampling interval by 2 doubles the expected error. Horizontally, we have an error of 23m, vertically maybe 5m. Sampling once per second, at walking speed (2m/sec) we get a measured speed "0  4 m/sec" i.e. just noise, at cycling speed we get a realistic speed "8  12 m/sec" or "1827 mph". Here, we can interpolate over longer time ranges (e.g. a moving average for 510 sec) to get an acceptable value for '(horizontal) current speed' but this loses all information necessary for a realistic "max speed" like we're used from the bike computer, supressing spikes. Vertically we have the double challenge that a) the vertical resolution of GPS is lower b) our vertical speed is significantly lower (exception: parachuting) and these two facts combine to GPS being completely useless for 'altitude gain' and 'vertical speed' in flat or rolling country. Rolf 
#44




GPS Units = Show road steepness?
On Tuesday, March 12, 2019 at 10:30:52 AM UTC4, Radey Shouman wrote:
Zen Cycle writes: Interesting how you characterize it as 'noise'. For the speedometer the main source of noise is quantization error, resulting from reducing a continuous wheel position to an integer number of revolutions. But that has to do with the digital filtering. I was under the impression that the ASICS most bike computer companies use calculate speed by the number of timing pulses between the wheel revolutions. As you mentioned in the other thread, even a 100hz timing pulse is going to give accurate results well beyond the typical 3 digit display of a bike computer. This is a simple math function rather than an a/d conversion, so I don't think quatization error applies here. Speed calculation could be considered a strict d/a, where the speed display is an analog number, yet derived purely as a digital process. There really isn't any 'noise' in speed calculations, except that even at a constant speed there would be some variation in the number of timing edges in between the wheel magnet triggers For the 2d field of altitudes obtained from a map I suspect that the quantization of position, ie, the limited number of data points, perhaps at irregular places, is the main source of noise. Here I can see the quantization error being an issue, since most bike computers use a barometric pressure transducer to detect altitude. Averaging is pretty critical here, and there is the issue of the transducer a/d then being processed back d/a for the display. As I mentioned above, short/steep gradients are more likely to be smoothed over intentionally to get rid of the quantization noise associated with attempting to oversample the transducer.. How to turn topographical survey data into something that looks like a continuous function is a whole field of study  there are many ways to go wrong, and no one perfect way to do it right. Sure, but I think that's way beyond the application requirements of a bicycle computer. There's no reason to over complicate the issue for us. If this was a military application, or something like flight computers in a passenger aircraft, the more accurate _and_ fast the better. On the issue of 'many ways to do it right'  My company builds products for oil and gas processing. Some of our products use use dual microprocessors in an nversion programming architecture. The outputs of both UPs have to give the same result, or the system shuts down  this is a failsafe application, not a life support system which would require redundant (fault tolerant) systems to keep people alive. In either case, errors that would be fairly small in altitude or distance become larger when differentiated to estimate speed or gradient. I think technology has progressed well beyond the point where that's an issue even in a cycling computer application. Remember, this whole conversation started because because a guy claimed his speed increased on flat ground without a tailwind or pedaling  the idea that he had the display set to average speed is much more plausible. 
#45




GPS Units = Show road steepness?
Zen Cycle writes:
On Monday, March 11, 2019 at 9:13:08 PM UTC4, Ralph Barone wrote: Radey Shouman wrote: Zen Cycle writes: On Sunday, March 10, 2019 at 6:35:02 PM UTC4, Roger Merriman wrote: Sir Ridesalot wrote: Talking about GPS units on another thread reminded me of something else I wondered if they do. Does a bicycle GPS unit show you the steepness of roads? There's an area that I frequently ride where on road has short but very steep hills, another road a mile or so east of it has much more gradual hills whilst a third road to the west of the first one is a major highway that can be ridden with a bicycle. What I'm wondering is this: if someone unfamiliar with the area got there and used a GPS unit to show those three roads, would the GPS unit show them the different gradients of the roads? Or is that another function that they'd need to download or otherwise install? Cheers Various mapping sites will show the gradient, and some GPS units will show the gradient, in the same way that it can give improbable maximum speeds they can also give improbable max gradients or sometimes on very short ramps not notice it, there is a nasty little ramp nr my folks place, which is the software flattens claiming 12% when itâ€™s a fair cruel 25/30% even more cruel this weekend with a 50mph headwind. It's probably an averaging issue  taking enough samples before and after the section so that it flattens the pitch. It's the same basic issue as the speedometer kerfluffle. Numerical differentiation amplifies noise. I would think it was the opposite. Numerical integration suppresses spikes. That's why I made the comment about the definition of 'noise'. I don't think differentiation is appropriate in this case, especially since we're doing simple math (not even algebra, let alone calculus). Speed and road gradient are both defined in terms of derivatives. These are approximated using "simple math". It seems a lot simpler if you haven't tried to do it  produce meaningful results, automatically, on schedule (meaing milliseconds or microseconds), all the time, from whatever data your machine has.  
#46




GPS Units = Show road steepness?
On 3/12/2019 7:30 AM, Radey Shouman wrote:
For the speedometer the main source of noise is quantization error, resulting from reducing a continuous wheel position to an integer number of revolutions. I'm pretty sure that counting revolutions is /not/ particularly relevant to modern electronic bike speedometers. For Odometer, probably much more relevant. For speed calculations, I'm strongly convinced that time between counts is used, with some division, as already noted earlier in this thread. After all, one rev. per second of a ~700c wheel comes to about 4.8 mph / 7.7 kph. Assuming you want the speedometer to update even once every two seconds, (I'm being generous here!) say in two seconds you get a count of 5 revolutions. That really means 5 to 5.99 or so revolutions occured in the two seconds, so a speed of 12 to 14.8 mph  not very impressive resolution. Faster updates lower the resolution. Averaging over multiple updates will improve resolution if speed is close to constant, but then you lose the ability to detect brief spikes (probably not a problem for a bike computer) and also get a bigger lag between speed changes and their reflection on the readout. I believe you're still right that quantization error is an issue, but with the resolution of the device's /clock/ as it times the gap between reed switch activations. Note this is all based on deduction of observed digital speedometer data and some fairly serious attempts at designing a DIY digital speedo back in the 70's, but not inside mfr information. I remember one design in a ?Popular mechanics? article that had one magnetize spokes and count them; 36 spokes per revolution versus one magnet really helped resolution. [One spoke per second (out of 36 spokes) is 0.133 mph, or equivalently, one spoke per 0.133 seconds is 1 mph, so count the spokes in 0.133 seconds and it's your speed in mph.] Quick updates and a simple design, but not up to our current standards for resolution, we'd likely count for 1.064 seconds and "divide" by 8. This was right around the time that quality stainless (nonmagnetizable) spokes came into wide use, though, trashing that idea. Cateye's original digital speedometer had you mount a ring at your hub with four magnets, perhaps to help the resolution problem; I owned one, and suspect they were already dividing by time interval, though. For the 2d field of altitudes obtained from a map I suspect that the quantization of position, ie, the limited number of data points, perhaps at irregular places, is the main source of noise. I agree. Gradient is in practice a very different calculation than speed, even though both are effectively numeric differentiation. How to turn topographical survey data into something that looks like a continuous function is a whole field of study  there are many ways to go wrong, and no one perfect way to do it right. In either case, errors that would be fairly small in altitude or distance become larger when differentiated to estimate speed or gradient. Yes, as ?you or others? noted above, numeric differentiation is known to magnify measurement/data errors. Mark J. 
#47




GPS Units = Show road steepness?
On 3/12/2019 12:46 PM, Mark J. wrote:
Â* Cateye's original digital speedometer had you mount a ring at your hub with four magnets, perhaps to help the resolution problem; I owned one, and suspect they were already dividing by time interval, though. I agree. I'll note in passing that the original Avocet cyclometers use a tiny (2"?) ring of 20 magnets to generate a wave signal using a coil pickup. It's quite a bit different from the clicks of a reed switch. IIRC, Jobst was in on that design. I doubt it's coincidence that he also had done a lot of toying around with ancient SturmeyArcher dynohubs, which also use a 20 magnet ring, although a much larger one. I've heard a rumor that the Avocet can get its signal directly from the SA magnets. But despite owning both, I haven't tried it.   Frank Krygowski 
#48




GPS Units = Show road steepness?
Zen Cycle writes:
On Tuesday, March 12, 2019 at 10:30:52 AM UTC4, Radey Shouman wrote: Zen Cycle writes: Interesting how you characterize it as 'noise'. For the speedometer the main source of noise is quantization error, resulting from reducing a continuous wheel position to an integer number of revolutions. But that has to do with the digital filtering. I was under the impression that the ASICS most bike computer companies use calculate speed by the number of timing pulses between the wheel revolutions. As As far as I can tell, none of us actually *know* how a bike computer works internally, we're all guessing, based on personal experience. you mentioned in the other thread, even a 100hz timing pulse is going to give accurate results well beyond the typical 3 digit display of a bike computer. This is a simple math function rather than an a/d conversion, so I don't think quatization error applies here. Speed calculation could be considered a strict d/a, where the speed display is an analog number, yet derived purely as a digital process. There really isn't any 'noise' in speed calculations, except that even at a constant speed there would be some variation in the number of timing edges in between the wheel magnet triggers If you look at the real wheel position versus time at constant speed, it is a line. The measured position, based on a signal from a reed switch, is a staircase. If you subtract the real position line from the staircase measured position line you get a sawtooth wave. The term of art for the difference between the measured and the actual signal is "noise". Quantization error is noise, noise is a property of a signal, not a calculation. For the 2d field of altitudes obtained from a map I suspect that the quantization of position, ie, the limited number of data points, perhaps at irregular places, is the main source of noise. Here I can see the quantization error being an issue, since most bike computers use a barometric pressure transducer to detect altitude. Averaging is pretty critical here, and there is the issue of the transducer a/d then being processed back d/a for the display. As I mentioned above, short/steep gradients are more likely to be smoothed over intentionally to get rid of the quantization noise associated with attempting to oversample the transducer. How to turn topographical survey data into something that looks like a continuous function is a whole field of study  there are many ways to go wrong, and no one perfect way to do it right. Sure, but I think that's way beyond the application requirements of a bicycle computer. There's no reason to over complicate the issue for us. If this was a military application, or something like flight computers in a passenger aircraft, the more accurate _and_ fast the better. On the issue of 'many ways to do it right'  My company builds products for oil and gas processing. Some of our products use use dual microprocessors in an nversion programming architecture. The outputs of both UPs have to give the same result, or the system shuts down  this is a failsafe application, not a life support system which would require redundant (fault tolerant) systems to keep people alive. Standards (and prices) for your companies products are much higher than for bike computers, obviously. In either case, errors that would be fairly small in altitude or distance become larger when differentiated to estimate speed or gradient. I think technology has progressed well beyond the point where that's an issue even in a cycling computer application. Sorry, that's nonsense. That differentiating amplifies (high frequency) noise is a mathematical fact that technology cannot change. Remember, this whole conversation started because because a guy claimed his speed increased on flat ground without a tailwind or pedaling  the idea that he had the display set to average speed is much more plausible. Oddly enough, whatever his display showed had to be some approximation of "average speed", preferably over some short interval. The Platonic ideal of the magnitude of the derivative of position is just not directly available to any of us mortals. And that ideal is what the laws of physics deal with.  
#49




GPS Units = Show road steepness?
On 3/12/2019 2:27 PM, Radey Shouman wrote:
Zen Cycle writes: Remember, this whole conversation started because because a guy claimed his speed increased on flat ground without a tailwind or pedaling  the idea that he had the display set to average speed is much more plausible. Oddly enough, whatever his display showed had to be some approximation of "average speed", preferably over some short interval. The Platonic ideal of the magnitude of the derivative of position is just not directly available to any of us mortals. And that ideal is what the laws of physics deal with. Yes, but the perfect Platonic ideal is not necessary for anything practical in cycling, not even for high budget racing. Current cyclometers tell speed to within 0.1 mph with a lag of no more than one second or so. They tell distance traveled with better accuracy. Nothing more is needed, even for detecting fantasies.   Frank Krygowski 
#50




GPS Units = Show road steepness?
On Tuesday, March 12, 2019 at 9:46:08 AM UTC7, Mark J. wrote:
On 3/12/2019 7:30 AM, Radey Shouman wrote: For the speedometer the main source of noise is quantization error, resulting from reducing a continuous wheel position to an integer number of revolutions. I'm pretty sure that counting revolutions is /not/ particularly relevant to modern electronic bike speedometers. For Odometer, probably much more relevant. For speed calculations, I'm strongly convinced that time between counts is used, with some division, as already noted earlier in this thread. After all, one rev. per second of a ~700c wheel comes to about 4.8 mph / 7.7 kph. Assuming you want the speedometer to update even once every two seconds, (I'm being generous here!) say in two seconds you get a count of 5 revolutions. That really means 5 to 5.99 or so revolutions occured in the two seconds, so a speed of 12 to 14.8 mph  not very impressive resolution. Faster updates lower the resolution. Averaging over multiple updates will improve resolution if speed is close to constant, but then you lose the ability to detect brief spikes (probably not a problem for a bike computer) and also get a bigger lag between speed changes and their reflection on the readout. I believe you're still right that quantization error is an issue, but with the resolution of the device's /clock/ as it times the gap between reed switch activations. Note this is all based on deduction of observed digital speedometer data and some fairly serious attempts at designing a DIY digital speedo back in the 70's, but not inside mfr information. I remember one design in a ?Popular mechanics? article that had one magnetize spokes and count them; 36 spokes per revolution versus one magnet really helped resolution. [One spoke per second (out of 36 spokes) is 0.133 mph, or equivalently, one spoke per 0.133 seconds is 1 mph, so count the spokes in 0.133 seconds and it's your speed in mph.] Quick updates and a simple design, but not up to our current standards for resolution, we'd likely count for 1.064 seconds and "divide" by 8. This was right around the time that quality stainless (nonmagnetizable) spokes came into wide use, though, trashing that idea. Cateye's original digital speedometer had you mount a ring at your hub with four magnets, perhaps to help the resolution problem; I owned one, and suspect they were already dividing by time interval, though. For the 2d field of altitudes obtained from a map I suspect that the quantization of position, ie, the limited number of data points, perhaps at irregular places, is the main source of noise. I agree. Gradient is in practice a very different calculation than speed, even though both are effectively numeric differentiation. How to turn topographical survey data into something that looks like a continuous function is a whole field of study  there are many ways to go wrong, and no one perfect way to do it right. In either case, errors that would be fairly small in altitude or distance become larger when differentiated to estimate speed or gradient. Yes, as ?you or others? noted above, numeric differentiation is known to magnify measurement/data errors. Mark J. How do you magnetize aluminum spokes? 
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