Sprocket Ratio = Pedal Assist MPH

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DrkAngel   10 GW

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Sprocket Ratio = Pedal Assist MPH

Post by DrkAngel » Jan 28 2012 7:37am

Note: Since investigating musical BPM, (Beats Per Minute), and discovering that, for training purposes, a musical BPM of double the crank-pedal RPM is recommended, I will revise my BPMs as RPMs.

For most builds, people should take into consideration the pedal assist capability of the bike.
(RPM - crank-pedal Revolutions Per Minute - pedal rate)
60 rpm is considered a casual-sustainable rate
90 rpm is, a more, top sustainable rate

Figured - rpm x ratio x wheel size" / inches per mile = mph

(rpm x 60min) x (Front T / Rear T) x (Wheel " x 3.14) /((12" x 5280' =) 63360) = mph

26" wheels - My EZip Trailz (OEM)
(60rpm x 60min) x (44T/14T) x (26" x 3.14) / (12" x 5280') = 14.57mph
(90rpm x 60min) x (44T/14T) x (26" x 3.14) / (12" x 5280') = 21.86mph

26" wheels - My EZip Trailz (w/32-11T upgrade)
(60rpm x 60min) x (44T/11T) x (26" x 3.14) / (12" x 5280') = 18.55mph
(90rpm x 60min) x (44T/11T) x (26" x 3.14) / (12" x 5280') = 27.83mph

26" wheels - My Black Widow (Upgraded 34-11T)
(60rpm x 60min) x (48T/11T) x (26" x 3.14) / (12" x 5280') = 20.24mph
(90rpm x 60min) x (48T/11T) x (26" x 3.14) / (12" x 5280') = 30.35mph

27" Wheels - My old 12 speed
(60rpm x 60min) x (52T/12T) x (27" x 3.14) / (12" x 5280') = 20.87mph
(90rpm x 60min) x (52T/12T) x (27" x 3.14) / (12" x 5280') = 31.31mph

700c = 28" wheels - My Haro Express Deluxe
(60rpm x 60min) x (48T/11T) x (28" x 3.14) / (12" x 5280') = 21.80mph
(90rpm x 60min) x (48T/11T) x (28" x 3.14) / (12" x 5280') = 32.69mph

29'er Wheels
(60rpm x 60min) x (48T/11T) x (29" x 3.14) / (12" x 5280') = 22.58mph
(90rpm x 60min) x (48T/11T) x (29" x 3.14) / (12" x 5280') = 33.86mph
Last edited by DrkAngel on Feb 26 2012 11:23am, edited 3 times in total.
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SoSauty   1 kW

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Re: Sprocket Ratio = Pedal Assist MPH

Post by SoSauty » Jan 29 2012 6:03pm

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Re: Sprocket Ratio = Pedal Assist MPH

Post by LI-ghtcycle » Jan 29 2012 8:27pm

DrkAngel wrote:For most builds, people should take into consideration the pedal assist capability of the bike.
(BPM - Beats Per Minute - pedal rate)
60 bpm is considered a casual-sustainable rate
90 bpm is, a more, top sustainable rate

Figured - bpm x ratio x wheel size = mph

(bpm x 60min) x (Front T / Rear T) x (Wheel " x 3.14) / 63360 = mph

26" wheels - My EZip Trailz (OEM)
(60bpm x 60min) x (44T/14T) x (26" x 3.14) / (12" x 5280') = 14.57mph
(90bpm x 60min) x (44T/14T) x (26" x 3.14) / (12" x 5280') = 21.86mph

26" wheels - My EZip Trailz (w/32-11T upgrade)
(60bpm x 60min) x (44T/11T) x (26" x 3.14) / (12" x 5280') = 18.55mph
(90bpm x 60min) x (44T/11T) x (26" x 3.14) / (12" x 5280') = 27.83mph

26" wheels - My Black Widow (Upgraded 34-11T)
(60bpm x 60min) x (48T/11T) x (26" x 3.14) / (12" x 5280') = 20.24mph
(90bpm x 60min) x (48T/11T) x (26" x 3.14) / (12" x 5280') = 30.35mph

27" Wheels - My old 12 speed
(60bpm x 60min) x (52T/12T) x (27" x 3.14) / (12" x 5280') = 20.87mph
(90bpm x 60min) x (52T/12T) x (27" x 3.14) / (12" x 5280') = 31.31mph

700c = 28" wheels - My Haro Express Deluxe
(60bpm x 60min) x (48T/11T) x (28" x 3.14) / (12" x 5280') = 21.80mph
(90bpm x 60min) x (48T/11T) x (28" x 3.14) / (12" x 5280') = 32.69mph

29'er Wheels
(60bpm x 60min) x (48T/11T) x (29" x 3.14) / (12" x 5280') = 22.58mph
(90bpm x 60min) x (48T/11T) x (29" x 3.14) / (12" x 5280') = 33.86mph
Good info, however, does it also take into account the extra torque needed for the higher speeds? The legs/motor still need to be able to maintain that kind of sustained power, and then there are the aerodynamic considerations, going from 20 MPH with X watts, isn't going to make 30 MPH with the same wattage even though you have mechanical advantage with gearing. :wink:
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DrkAngel   10 GW

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Re: Sprocket Ratio = Pedal Assist MPH

Post by DrkAngel » Jan 29 2012 8:57pm

Yeah, I found a nice program, too ... after I did the figuring ...
Bicycle gear size and cadence/speed calculator
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There, shallow draughts intoxicate the brain,
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DrkAngel   10 GW

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Re: Sprocket Ratio = Pedal Assist MPH

Post by DrkAngel » Jan 30 2012 8:12am

LI-ghtcycle wrote:
Good info, however, does it also take into account the extra torque needed for the higher speeds? The legs/motor still need to be able to maintain that kind of sustained power, and then there are the aerodynamic considerations, going from 20 MPH with X watts, isn't going to make 30 MPH with the same wattage even though you have mechanical advantage with gearing. :wink:
No, just pedal speed capability.

However ... variations of motor and gearings show the following, (real world), motor only top speeds, for my mountain bike style:
450 watt = 21-22 mph
675 watt = 27 mph
750 watt (1HP) = 30 mph
832 watt = 32 mph? (estimated from 44.4V pack)
(based on Li-ion batteries w/full charge)
"watts" are motors output watts ... not input watts.

I, of course, would like to keep my pedal assist capability, at noticeably past , motor only speed.
There is still motor assist applied, past the motor only speed ... it's just waiting ... for a little help, from me!

I can push my 675 watt, (27mph), EZips, past 30 mph, even to 35mph ... with a tailwind, or drafting.
Last edited by DrkAngel on Aug 03 2014 10:30am, edited 2 times in total.
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There, shallow draughts intoxicate the brain,
And drinking largely, sobers us again.

I enjoy enlightening ... and enlivening the spirit of the innovators.

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DrkAngel   10 GW

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Re: Sprocket Ratio = Pedal Assist MPH

Post by DrkAngel » Feb 02 2012 4:06pm

DrkAngel wrote: No, just pedal speed capability.

However ... variations of motor and gearings show the following, (real world), motor only top speeds, for my mountain bike style:
450 watt = 21-22 mph
675 watt = 27 mph
750 watt (1HP) = 30 mph
832 watt = 32 mph? (estimated from 44.4V pack)
(based on Li-ion batteries w/full charge)
"watts" are motors output watts ... not input watts.

I, of course, would like to keep my pedal assist capability, at noticeably past , motor only speed.
There is still motor assist applied, past the motor only speed ... it's just waiting ... for a little help, from me!

I can push my 675 watt, (27mph), EZips, past 30 mph, even to 35mph ... with a tailwind, or drafting.
One of my earlier graphs:
Demonstrates 24V(450w) & 36V(675w) and various gearing.
"Road Load-Wind Resistance" - green line - can be used to project, similar build, capability-speeds.
(48V(900w) 20T or 44.4V(832w) 16T = +30mph motor only)

Image
Last edited by DrkAngel on Aug 03 2014 10:30am, edited 1 time in total.
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There, shallow draughts intoxicate the brain,
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DrkAngel   10 GW

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Re: Sprocket Ratio = Pedal Assist MPH

Post by DrkAngel » Feb 02 2012 11:45pm

DrkAngel wrote: One of my earlier graphs:
Demonstrates 24V(450w) & 36V(675w) and various gearing.
"Road Load-Wind Resistance" - green line - can be used to project, similar build, capability-speeds.
(48V(900w) 20T or 44.4V(832w) 16T = +30mph motor only)

Image
Most DC motor, Watt output (HP) graphs show highest output at 40-50% of no load speed.
Substantial assist plummets near 85% of no load speed
For example, the 36V w/16T mod, no load, speeds at 34mph.
WOT, level travel, motor only, provides, approximately, 27mph which figures at 80% of no load speed.
Which indicates max possible speed from the 675w output motor.

This motor is optimally geared for highest motor only speed.
Gearing for higher speed would decrease motor only speed, but increase, combined, motor & pedal assist, speed.
Last edited by DrkAngel on Feb 22 2013 10:02am, edited 1 time in total.
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There, shallow draughts intoxicate the brain,
And drinking largely, sobers us again.

I enjoy enlightening ... and enlivening the spirit of the innovators.

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DrkAngel   10 GW

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Human power - watts/duration

Post by DrkAngel » Feb 10 2012 7:44am

Human power. Healthy male vs trained athlete.
Possible power output (watts), for various durations.

A nice guide, towards estimating, pedal assist contribution.
humanL.JPG
humanL.JPG (38.26 KiB) Viewed 1689 times
Very revealing, to me, was that a "Healthy Male", was capable of 200w output, for 30 minutes, while the "First Class Athlete" was capable of the same 200w output ... for 20 hours!
Last edited by DrkAngel on Feb 16 2012 5:29pm, edited 1 time in total.
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There, shallow draughts intoxicate the brain,
And drinking largely, sobers us again.

I enjoy enlightening ... and enlivening the spirit of the innovators.

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Re: Human power - watts/duration

Post by Architectonic » Feb 12 2012 5:29am

DrkAngel wrote:A nice guide, towards estimating, pedal assist contribution.
Wow, where did you find this image?

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DrkAngel   10 GW

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Re: Human power - watts/duration

Post by DrkAngel » Feb 12 2012 8:34am

Architectonic wrote:
DrkAngel wrote:A nice guide, towards estimating, pedal assist contribution.
Wow, where did you find this image?
Pulled it from an independent, eMotorcycle developer, site.
Kraig Schultz’s Opinions on Aerodynamics and Electric Motorcycles

Much more too ...

All the reason, I needed, to consider a modest fairing-windscreen ...
AeroShapes.JPG
AeroShapes.JPG (12.33 KiB) Viewed 1553 times
Drag , via bicycle type - 22mph
AerodynamicsL.JPG
AerodynamicsL.JPG (81.43 KiB) Viewed 1553 times

Click on picture, then "+" sign to obtain readable chart!
drag_chart.jpg
This site has been a major inspiration, for my eMotorcycle build!

Yes, eventually, I "must" add a shroud-fairing!
d-11-vs-125.jpg
d-11-vs-125.jpg (30.99 KiB) Viewed 1553 times
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There, shallow draughts intoxicate the brain,
And drinking largely, sobers us again.

I enjoy enlightening ... and enlivening the spirit of the innovators.

New & Improved - Acronym Definitions

Index - Homemade Battery Packs - Updated - November 2018

EBike Toolbox - Bargains! $

Endless Sphere Wiki - Lost?

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