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# Question on calculating distance

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# Question on calculating distance

10-25-21, 10:17 AM
#1
coco1854
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Question on calculating distance

Hi

I have an old computrainer, and I'm curious how it calculates distance. My wheels are standard 26" (~ 66 cm).

My back of the envelope calculation for a 16.1 km time trial that I just did is: 66 x 3.14 x 88 (average rpm). This gives me ~ .182 km/min. I finished the time trial in 32 min. But .182 x 32 is ~ 5.82. What am I doing wrong ?

Thanks a lot in advance.
10-25-21, 11:01 AM
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blacknbluebikes
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Could you rephrase your question as a question? you're asking about distance? but you know the distance? are you asking about speed?
10-25-21, 11:04 AM
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10 Wheels
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Riding inside on a Trainer is TIME Only. No Miles
Because YOU Really Don't Roll Miles.
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Last edited by 10 Wheels; 10-25-21 at 11:22 AM.
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10-25-21, 11:19 AM
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unterhausen
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A wheel-on trainer knows how far you went because it can count the revolutions of the pick up wheel and multiply by the circumference of the pick up wheel. It has nothing to do with the wheel size of your bike.
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10-25-21, 01:03 PM
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coco1854
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Originally Posted by unterhausen
A wheel-on trainer knows how far you went because it can count the revolutions of the pick up wheel and multiply by the circumference of the pick up wheel. It has nothing to do with the wheel size of your bike.
1) And how does it know the circumference ? I assume it takes the diameter of a standard wheel -- 26" -- and multiplies it by 3.14. That's how you get the circumference of any circle.

2) My confusion is; if I multiply the circumference by the revolutions per minute (my pedaling cadence) and multiply that by the the number of minutes it took me to finish the course, I should get the total distance of the course. But when I do that calculation -- circumference x rpm x minutes to finish the course -- I get ~ 5.84 km. But the length of the course, according to the software is 16.1 km
10-25-21, 01:09 PM
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gthomson
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Originally Posted by unterhausen
A wheel-on trainer knows how far you went because it can count the revolutions of the pick up wheel and multiply by the circumference of the pick up wheel. It has nothing to do with the wheel size of your bike.
Well that's not totally true, based on how bike computers used to calculate distance before GPS existed. So I still have a Vetta bike computer on my old 1980's Peugeot and for it to calculate speed and distance, you need to enter the wheel size which it then does some calculation along with RPM of wheel. I'm no mathematician so won't even attempt to tell you how it all works but I'm sure someone on those forum can.
You also have to enter your wheel size when you configure your trainer on Zwift.

Though I'm not really sure what the OP is asking so maybe he's referring to something totally different.

This is the original guide it came with.
Attached Files
Vetta_C300_manual .pdf (1.27 MB, 0 views)

Last edited by gthomson; 10-25-21 at 02:09 PM.
10-25-21, 01:20 PM
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spelger
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Originally Posted by coco1854
1) And how does it know the circumference ? I assume it takes the diameter of a standard wheel -- 26" -- and multiplies it by 3.14. That's how you get the circumference of any circle.

2) My confusion is; if I multiply the circumference by the revolutions per minute (my pedaling cadence) and multiply that by the the number of minutes it took me to finish the course, I should get the total distance of the course. But when I do that calculation -- circumference x rpm x minutes to finish the course -- I get ~ 5.84 km. But the length of the course, according to the software is 16.1 km
is this a single speed ride? even so, you need to know the gear ratio. crank RPM is not the same as wheel RPM.
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10-25-21, 01:22 PM
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spelger
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Originally Posted by 10 Wheels
Riding inside on a Trainer is TIME Only. No Miles
Because YOU Really Don't Roll Miles.
i love these silly answers. everyone who rides a trainer of any sort knows they are not riding any distance or climbing any elevation. we get that it is all virtual or simulated. but there sure is a hell of a lot of effort going nowhere though.
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10-25-21, 01:29 PM
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10 Wheels
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Originally Posted by spelger
i love these silly answers. everyone who rides a trainer of any sort knows they are not riding any distance or climbing any elevation. we get that it is all virtual or simulated. but there sure is a hell of a lot of effort going nowhere though.
Many think they are riding miles
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10-25-21, 03:07 PM
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spelger
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Originally Posted by gthomson
Well that's not totally true, based on how bike computers used to calculate distance before GPS existed. So I still have a Vetta bike computer on my old 1980's Peugeot and for it to calculate speed and distance, you need to enter the wheel size which it then does some calculation along with RPM of wheel. I'm no mathematician so won't even attempt to tell you how it all works but I'm sure someone on those forum can.
You also have to enter your wheel size when you configure your trainer on Zwift.

Though I'm not really sure what the OP is asking so maybe he's referring to something totally different.

This is the original guide it came with.
i think he is just comparing the CompuTrainer distance with what he calculated. sort of a sanity experiment. problem is that he needs to know the wheel RPM, and not his cadence (crank RPM), and that is not easily calculable if only avg cadence is available.
10-25-21, 03:48 PM
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grizzly59
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If you are riding with a 42 tooth chainring and 15 tooth cog that would be pretty close. Your 66cm dia might be a bit high.
10-25-21, 04:00 PM
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Originally Posted by coco1854
1) And how does it know the circumference ? I assume it takes the diameter of a standard wheel -- 26" -- and multiplies it by 3.14. That's how you get the circumference of any circle.

2) My confusion is; if I multiply the circumference by the revolutions per minute (my pedaling cadence) and multiply that by the the number of minutes it took me to finish the course, I should get the total distance of the course. But when I do that calculation -- circumference x rpm x minutes to finish the course -- I get ~ 5.84 km. But the length of the course, according to the software is 16.1 km
You're missing a number, which is the conversion of your cadence to revolutions of the wheel. Even if you rode in a single gear the whole time, turns of the crank do not equal turns of the wheel. What gear did you run, front and rear?
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10-25-21, 04:05 PM
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Bald Paul
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Originally Posted by 10 Wheels
Many think they are riding miles
When I was an auto tech, we would often have to run a car in gear while up on a lift.
Even though the car wasn't going anywhere, the odometer still changed.
10-25-21, 04:06 PM
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genejockey
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Originally Posted by grizzly59
If you are riding with a 42 tooth chainring and 15 tooth cog that would be pretty close. Your 66cm dia might be a bit high.
Not only that, but it's calculated wrong. 26" wheels are not 26" in diameter, AND the circumference figure has to include the tire. That's why cyclocomputer manuals used to have you measure the circumference with a rollout test. So, there are a number of numbers missing or incorrect in his calculation.
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10-25-21, 05:44 PM
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unterhausen
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Originally Posted by coco1854
1) And how does it know the circumference ? I assume it takes the diameter of a standard wheel -- 26" -- and multiplies it by 3.14. That's how you get the circumference of any circle.
Originally Posted by gthomson
Well that's not totally true, based on how bike computers used to calculate distance before GPS existed. .
The trainer knows how far the trainer went. It doesn't care about the circumference of the bike wheel at all. It cares about the circumference of the part of the trainer that the bike wheel rides on and the number of rotations that part has made.

I agree that the distance on a trainer isn't particularly important, but in this case there is an actual distance traveled and it's measured directly by quantities known by the trainer designer. You could drive it with a penny farthing and it wouldn't matter what the wheel diameter of the bicycle was.

I'm not sure if there is anything wrong with the OP's calculation. Maybe there is a lot of slippage. But the distance given by the trainer is the circumference of the friction wheel times the number of rotations that it has made. Simple as that. No bike wheel size needs to be involved at all to know that.
10-25-21, 06:43 PM
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https://www.cateyeamerica.com/tire-size-calculator/

So just for sport-

26" wheel- I'll estimate a 1.5x26 (40-559) tire, rolling circumference 2005mm per Cateye
88 RPM ave cadence
42 chainring 15 cog = 2.8 ratio (my reasonable guess)
16.1 km TT

rate = 2005 x 88 x 2.8 = 494.03 M/min
time = 16100 / 494.03 = 32.58 min, in the ballpark

If your rolling circumference was 2042 then with the above your time would be 31.99 min

Last edited by grizzly59; 10-25-21 at 07:03 PM.
10-25-21, 10:03 PM
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I once was in a Large Club that tracked Real Miles. Some tried to Add Training Miles.
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10-26-21, 06:41 AM
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coco1854
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Originally Posted by genejockey
You're missing a number, which is the conversion of your cadence to revolutions of the wheel. Even if you rode in a single gear the whole time, turns of the crank do not equal turns of the wheel. What gear did you run, front and rear?

I subsequently realized I had omitted this. I rode the whole time in the highest gear -- 41 (chainring) and the smallest cog on the rear cassette, which is either 14 or 15 (it's a seven cog cassette). So the equation now makes sense. But, of course, the software had no way of knowing the available gear ratios on my bike, let alone which ones I choose to use.

Do you know what assumptions about gearing training software usually makes (I'm using an old computrainer)? Obviously for hilly sessions, it will assume a lower gear ratio than for time trials, but it doesn't know my specific bike nor the gear ratio that I choose.

Thanks

Last edited by coco1854; 10-26-21 at 06:54 AM.
10-26-21, 06:58 AM
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Originally Posted by 10 Wheels
Many think they are riding miles
For years, I never viewed trainer time as me riding miles. Then I started zwifting and it suddenly changed to me viewing trainer time as me riding miles since the little dude sure did cover a bunch of distance on the screen.
Virtual miles?...sure, call them that if you need.
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10-26-21, 01:30 PM
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Originally Posted by coco1854
Do you know what assumptions about gearing training software usually makes (I'm using an old computrainer)? Obviously for hilly sessions, it will assume a lower gear ratio than for time trials, but it doesn't know my specific bike nor the gear ratio that I choose.
Are you still trying to figure out how the trainer calculates distance? It doesn't need to know anything about your bike.
10-26-21, 01:54 PM
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coco1854
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I am. How can the computer know how far I've gone if it doesn't know my gear ratio or the circumference of my wheel ?
10-26-21, 01:56 PM
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coco1854
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Excellent caluculation ! My actual time was 32:04. Tbh, I think the final avg cadence was 89 rpm.
10-26-21, 03:04 PM
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Bald Paul
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Originally Posted by 10 Wheels
I once was in a Large Club that tracked Real Miles. Some tried to Add Training Miles.
Miles are miles, no matter what the club said.
If you don't believe me, put your car on jack stands and run it in gear for 100,000 miles. Then bring it to your dealer for warranty and tell them the odometer doesn't show "real miles".
10-26-21, 03:07 PM
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Originally Posted by coco1854
I am. How can the computer know how far I've gone if it doesn't know my gear ratio or the circumference of my wheel ?
I'm not sure if I can explain it any differently than I previously have. The bike's wheel rides on a part of the trainer that is also a wheel. That trainer part has a circumference. They just count the number of rotations that part of the trainer has done, multiply it by its circumference, and that is your distance. They can also use it for speed. If you could turn that wheel by hand with the bike off the trainer, the trainer would still give you a speed and distance.
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10-26-21, 03:14 PM
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genejockey
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Originally Posted by coco1854
I am. How can the computer know how far I've gone if it doesn't know my gear ratio or the circumference of my wheel ?
It "knows" the circumference of the drum your tire spins against. Whatever that circumference is, times the number of times it goes around, is the distance you've "travelled". The Computrainer doesn't know how many times your wheel went around, so it can't use the circumference of your wheel in any case.
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