Wheel diameter to speed/RPM chart

[spinningmagnets]

When contemplating a non-hub motor, the maximum motor RPM target and gearing equations can get complex. By selecting the lowest top speed that can satisfy your performance needs, torque will be maximized across the resulting rpm band.

From reading here, most builders have settled on wheel diameter and top speed desired when they begin pondering motor Kv selection, voltage to be used, and gear-down options. I have compiled this chart to make the process a little easier.

This link is a pedal cadence calculator (thanks, Drunkskunk), but if the sprocket and chainring tooth-count numbers entered are the same (1:1) then the pedal-cadence will be the same as the rear-wheel rpm.

http://www.machars.net/bikecalc.htm

If you want to use a tire with an odd outside diameter (such as a fat moped tire on a 20-inch bicycle wheel, which would typically be 22-inches), you go to the tire selection and click on “other", then enter a number of the tire outside diameter into the next square in inches (decimals allowed, 1/4-inch is 0.25).

For instance, if using a custom tire with an outside diameter of 60-centimeters, you would use an online conversion calculator, then enter the result of 23.62 (inches) into the cadence calculator Other---> wheel (using 1:1 gears) to find the top-speed/rpm result. Suggestions welcome...
________________________________________
Here's another method:

(10 mph x 5280 feet/mile) / 60 min per hr = 880 feet per min, so...10-MPH = 880 feet per minute

The diameter of the wheel is X inches. In one revolution, it travels a distance equal to the circumference of the wheel, which is Pi times the diameter:
(X inches x 3.14159) / 12 inches = Y feet (if X is 26-inches, Y = 6.81 feet)

Then we just calculate the number of revolutions needed to travel 880 feet:
(880 feet/min) / (Y feet/rev) = Z RPM (880 / 6.81 = 129.3 RPMs for 10-MPH)...which is equal to 12.9 for 1-MPH

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http://www.onlineconversion.com/

1 mph = 1.609 kph
1 kph = 0.621 mph

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29 inch tire

11.6 RPM per one-MPH

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27.5 inch tire

12.2 RPM per one-MPH

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26-inch tire
1 mph = 12.93 rpm
1 mph = 1.609 kph
1 kph = 8.10 rpm

MPH (km/h) = RPM
01__(1.61)___12.9
02__(3.22)___25.9
03__(4.83)___38.8
04__(6.44)___51.7
05__(8.05)___64.7
06__(9.65)___77.6
07__(11.26)__90.5
08__(12.87)__103.4
09__(14.48)__116.4
10__(16.09)__129.3
11___(18)___142
12___(19)___155
13___(21)___168
14___(23)___181
15___(24)___194
16___(26)___207
17___(27)___220
18___(29)___233
19___(31)___246
20___(32)___259
21___(34)___272
22___(35)___285
23___(37)___297
24___(39)___310
25___(40)___323
26___(42)___336
27___(43)___349
28___(45)___362
29___(47)___375
30___(48)___388
31___(50)___401
32___(51)___414
33___(53)___427
34___(55)___440
35___(56)___453
36___(58)___465
37___(60)___478
38___(61)___491
39___(63)___504
40___(64)___517
MPH (km/h) = RPM


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24-inch tire
1 mph = 14.00 rpm
1 mph = 1.609 km/h
1 kph = 8.80 rpm

MPH___(km/h)___RPM
01__(1.61)___14
02__(3.22)___28
03__(4.83)___42
04__(6.44)___56
05__(8.05)___70
06__(9.65)___84
07__(11.26)__98
08__(12.87)__112
09__(14.48)__126
10__(16.09)__140
11___(18)___154
12___(19)___168
13___(21)___182
14___(23)___196
15___(24)___210
16___(26)___224
17___(27)___238
18___(29)___252
19___(31)___266
20___(32)___280
21___(34)___294
22___(35)___308
23___(37)___322
24___(39)___336
25___(40)___350
26___(42)___364
27___(43)___378
28___(45)___392
29___(47)___406
30___(48)___420
31___(50)___434
32___(51)___448
33___(53)___462
34___(55)___476
35___(56)___490
36___(58)___504
37___(60)___518
38___(61)___532
39___(63)___546
40___(64)___560
MPH (km/h) = RPM


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22 inch diameter tire (Pirelli ML75 moped tire on a 20-inch rim)

15.3 RPM per one-MPH

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20-inch tire
1 mph = 16.81 rpm
1 kph = 10.50 rpm

10 mph (16 kph) = 168 rpm
11 (18) = 185
12 (19) = 202
13 (21) = 219
14 (23) = 235
15 (24) = 252
16 (26) = 269
17 (27) = 286
18 (29) = 303
19 (31) = 319
20 (32) = 336
21 (34) = 353
22 (35) = 370
23 (37) = 387
24 (39) = 403
25 (40) = 420
26 (42) = 437
27 (43) = 454
28 (45) = 471
29 (47) = 488
30 (48) = 504

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16 inch tire

21 RPM per one-MPH

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[jdcburg]

Spinning magnets - Nice work. I've attached a little Excel table that is less detailed but more compact. Also it includes 700c tires. Another tack would be to use http://www.arachnoid.com/bike/ to do some calculations for you. You can put your motor rpm in where it says pedal cadence, your motor sprocket where it says front sprocket teeth and up to 12 potential rear sprockets where it says rear sprocket teeth to see the effect of different sprockets. You can even put up to 4 motor sprocket sizes in - jd

 

[spinningmagnets]

Excellent chart sir! Very useful, thank you. I think the gear calculator link that you provided is a little easier to use for the most frequent gearing questions compared to the well-known Sheldon Browns Bicycle Gear Calculator, but just for laughs, here it is also:

http://sheldonbrown.com/gears/index.html

 

[Russell]

While the chart is good for getting in the ballpark in practice the overall diameter of a 700C tire for example varies greatly depending on the size. Therefore I simply use a little math to calculate speed at various RPM's, or vice-versa.

Example: 700C x 50mm

Diameter = 622mm + (2 x 50mm) = 722mm
Circumference = 722mm x 3.1416 = 2268mm
Divide circumference by 25.4 to get inches then that number by 12 to get feet or 7.44 ft

With that you can calculate the speed for any RPM

For 250 RPM;

7.44 ft/rev x 250 rev/min x 60 min/hr x 1 mi/5280 ft = 21.1 MPH

or if say you know the speed is 20 MPH then solve for RPM;

20 mi/hr x 5280 ft/mi x 1 hr/60 min x 1 rev/7.44 ft = 237 RPM


You can also easily calculate bike speed at various pedaling cadences

For example say I pedal at 90 rev/min with a 42 front chainring and 13 tooth rear cog using that same 700C x 50mm tire;

42/13 = 3.23

3.23 x 90 rev/min x 7.44 ft/rev x 1 mi/5280 ft x 60 min/hr = 24.6 MPH


-R

 

[DasDouble]

subscribed 8)

 

[deronmoped]

Here is a great calculator from "Electric Scooter Parts", there are actually two of them, a Top Speed and Gear Ratio Calculator for a non jack shaft type and a Jack shaft type. Just input the motor speed, gears and tire diameter, it gives you the gear ratio and speed. http://www.electricscooterparts.com/motor-jackshaft-wheel-gear-ratio.html

 

[ColdRider]

That's great tool and works well too Thanks Spinningmagnet ,Here is a tool I did use many times it may lack extreme precision but has served me well over time ,I find it long to fill in but that is what a Hobbyist/Enthousiast DIY E-Biker want at least thats what I got ->Fun

-> http://cyclurba.fr/braquet.php

Enjoy

 

[spinningmagnets]

Merci beaucoup, mon ami.

[Thank you, my friend.]

 

[atarijedi]

Here is a tool I use to calculate speed, RPM, etc...

http://www.advanced-ev.com/Calculators/TireSize/

For hub motors, you put the differential at 1, for non-hub motors, you need to put the total ratio from motor to rear wheel.

 

[JackElliott]

Good stuff. Anyone make a similar but for IGHs?

 

[Chalo]

Sheldon Brown's internal gear calculator will give output as pedal RPM per speed and speed per pedal RPM, as well as other formats.

Here's a road speed calculator I've used for many years: http://www.4qd.co.uk/road-speed-calculator/

 

[eCue]

The road speed calculator in Chalo's above post works well , for newbies with a Hub motors enter the wheel size , the motors RPM rating and use 1 for the reduction gear number and it will give the speed estimate.

 

[WizardDave]

What if I want to make a Gilligan's island generator? meaning take a bicycle or a even an exercise bike and hook a belt around the drive rim, with no tire on, it just the rim, connected to a car alternator. How do I figure out how fast I need to either pedal or how big your how small the pulleys I need to use to hook to a alternator to put out decent enough amps for a 12-volt charge? I know that most alternators require a minimum of around 2,000 RPM

 

[amberwolf]

How fast can you normally ride the bicycle in question, in a gear that is comfortable for you to sustain that effort, for as long as you would need to use it as a generator? (Keep in mind that if you need your generator to supply 1000w of power, you have to input more than that by pedalling, so you won't be able to do it for very long...most people can only do about 100w of effort or so for any length of time).

Also remember that an alternator on a car isn't really 12v, it's typically 14-15v unloaded, and "standard" average voltage should be around 13.6v when loaded.

Once you know that speed, then measure the circumference of the actual inflated tire on the rim first, and save that number. A 26" wheel with tire is probably around 80-90-something inches.

Then measure the circumference of the rim in inches (or mm, etc), inside it where the belt would ride. This will tell you the "size" of it as a pulley, and let you use this number to determine the RPM it would have at the speed you were riding at above. A 26" rim without tire is probably around 70 inches.

RPM would be the number of times the wheel will spin in one minute; vs the speed you were riding at which is in miles per hour (or kilometers per hour, but we'll use MPH for this). Convert to miles per minute by multiplying the MPH by 60. Convert the mile to rim circumference (to determine number of rotations for the distance) by multiplying the miles by 5280 feet per mile, then 12 inches per foot, to get inches (which you can convert to mm if that's what you measured the rim circumference in), which should be around 63360 inches a minute for 1mph. Then divide that by the circumference of the wheel, which if it's 90 inches, would be 63360 / 70 is 700 rotations per mile.

This page https://itstillruns.com/calculate-wheel-speed-tire-diameter-7445086.html
gives the steps better than my exhausted brain.

Now divide the inflated tire circumference by the rim circumference, and multiply the RPM above by that number (to get the difference between wheel size with and without a tire on it).


For a 26" wheeled bike at around 20mph, you'll probably get a number in the 250-300-ish RPM range. So if you have a 2000 RPM output requirement, you would need a pulley on the generator end that is about 300 divided by 2000 times smaller than the bike rim, or around 10 inches in circumference, which is something like 3 inches in diameter.

If you can only sustain 10mph, it'll probably be around 150 rpm, so the generator pulley would need to be half the size to increase the gearing ratio by double to keep the same generator speed, so around 5 inches in circumference, which is something like an inch and a half diameter.

You'll have to do the math for your specific situation and parts, and probably experiment a bit, to get the final actual pulley size for the generator.

 

[Balmorhea]

What if I want to make a Gilligan's island generator? meaning take a bicycle or a even an exercise bike and hook a belt around the drive rim, with no tire on, it just the rim, connected to a car alternator. How do I figure out how fast I need to either pedal or how big your how small the pulleys I need to use to hook to a alternator to put out decent enough amps for a 12-volt charge? I know that most alternators require a minimum of around 2,000 RPM

I found it was easier to use a brushed DC scooter motor. There are a lot of them in 24 to 48VDC and in the 2400 to 3000 RPM range, which means you only have to spin them 1/4 to 1/2 as fast to get 12V of back emf.

Most use chains, but that saves you a variety of headaches and inefficiencies anyway.

http://tncscooters.com/index.php?route=product/product&product_id=332

If I had it to do over again, I'd use a brushed DC hub motor, to get the RPM down even more for quietness and simplicity.