DrkAngel

Some of my earlier graphs hinted at the watts-HP required to attain specific speeds.
I thought it might be handy to build a chart with specific watt requirements for various bike types to attain various speeds.

First graph limited in range to allow better visibility.

2nd charted to 50mph.

Mountain Bike 50MPH = 4280w

turbo1889

His charts match up with my calculations, assuming no tail/head wind, flat ground, and a "normal" bike weight, aerodynamic profile, and wheel drag.

So I'm confirming his results within a narrow window of application, also input watts do not equal output watts, you have to take the efficiency into consideration as well and the efficiency of a motor is not constant along its entire power range and the efficiency numbers that motor manufactures give are usually peak efficiency and through most of the usable power range efficiency is usually less then peak. Just saying.



Edit: Would also note that his graphs seem to be spaced on input specs. that are a little on the conservative side. I've been able to reach 27-mph on the flat in calm air with a bike that was by no means a road bike or recumbent or anything close that that and was definitively more along the MTB line that was limited to 640 watts maximum input to the motor (50-amps limited by the controller at 12.8-volts) with a motor that according to the specs and my calculations was operating at less then 85% efficiency. So depending on your build you might get a little more speed out of your build for the power then his graphs indicate, but its certainly not something you can count on. And I wouldn't say you can count on getting the speed his graphs indicate either, just wearing a bulky full length coat in the winter can produce a noticeable drag that will slow you down from the extra air drag. They are good rule of thumb guides though and its good to set the variables to a little on the conservative side for such.

christo930

What weight are you using for this graph (bike + motor + battery + human)?

Chris

turbo1889

Weight actually doesn't matter all that much for top speed on the flat. Weight only slightly increases the rolling resistance at speed when the rolling resistance is the minor factor to be overcome, air resistance actually is the larger factor. Of course more weight takes longer to accelerate up to speed but doesn't make a huge difference in the actual top speed.

Now when it comes time to go up a hill, that is when the weight is the critical factor.

I've got an XL spreadsheet will all the calculations built in so you can adjust weight and air resistance coefficients and rolling drag coefficients and go up or down hills of varying slope and with head winds or tail winds and adjust all that stuff.

DrkAngel

Weight is based on a representative average for each type.

Weight is reflected as a slight fluctuation in the Rolling Resistance.
But ... weight is a comparatively minor factor at speeds above 20mph ... for level travel with tires at pressure.

As demonstrated in the following graph,
wind resistance is a geometric progression while
road load-rolling resistance is a simple linear progression.



* Rolling Resistance is factored from a representative mountain bike tire.

DrkAngel

A Mountain bike requires 255w of pedal effort to maintain 18mph.
I chose 18mph because most cyclists are familiar with the effort required to maintain this speed.

This graph demonstrates the additional speed available from adding the effort required to power a bicycle at 18mph.


From 10mph, assist will double speed to 20mph (10mph).
From 20mph, the same amount of pedal assist will increase speed 5mph.
From 30mph, the same amount of pedal assist will increase speed 2.5mph.
From 40mph, the same amount of pedal assist will increase speed <2mph.
However at 50mph, the same amount of pedal assist will increase speed ... barely ... 1mph!

On the other hand ...
This degree of pedal assist will more than triple range (300%) at 20mph and almost double range (200%), cruising at 25mph.
At 30mph assist increases range, possibly 33% (133% total).
Pedal assist contribution percentage declines quickly with speed.
Near 30mph, a more aerodynamic position outperforms even substantial pedal assist from a "proper" pedal seating position.

Even a race bike with cyclist in tuck position demonstrates the aerodynamic advantage clearly.

DrkAngel

My charts-graphs refer to a motors, or humans, watts of energy output ... not watts of electrical input.

While eBike motor systems are capable of 80-90% efficiency, at peak watt-HP output 50% efficiency is more typical!

Peak HP-watt output occurs at near to 40-45% of motors top no-load speed.
Peak motor output is at a 50% efficiency, 500w motor output requires 1000w electrical input.

~80% efficiency is available ... at top attainable speed, about 21mph, but motor watt output is reduced to 350w - from a 465w electrical input.

turbo1889

^ Depends on the motor.

Not all have graphs that look like that, especially better performance rare-earth magnet brush-less motors with low resistance motor coils which can have a peak power output point that is both well above the 50% RPM zone and 50% efficiency zone. I have yet to see a motor that exceeded both the 75% RPM and 75% efficiency zone at its peak power output point on its graph. I have seen quite a few though with "useful" power levels produced at inefficiencies at or exceeding 75%. Although I love the simplicity of DD hubs, especially when used in a Stoker-Monkey frame mount mid-drive assembly they don't tend to have the best looking graphs of the available motors. Motors designed to run at higher RPMs with a gear reduction tend to push the peak power point higher up both the RPM and efficiency scale for where the peak power point occurs. There is also some controller effect in there as well since some controllers especially those capable of independently limiting current draw on the motor side not just the battery side can change things noticeably.

You are generally correct though that you usually want a bigger motor then the wattage you will usually be pulling so you can enough power for your needs while the motor is in its higher efficiency zone.

phoebeisis

How much hp or watts can a good bike rider sustain-pedaling a bike-for say 1 minute?
Can anyone actually hold 33 mph at sea level-1 hp 750 watts-for a minute?

I seem to remember the "pilot/motor" of that English Channel human powered plane was producing under 1/2 hp-for 1.5 hrs or so?? He was a bike rider.
Not Lance at his most boosted of course-heck not Lance Unboosted.

DrkAngel

Track record is a sustained 32mph for 1 hour!

This graph documents sustainable outputs ...

phoebeisis

Thanks!
So 32mph- ALL BUT 1 HP for in hour! Obviously a freakish athlete on a "not average" bike!
Didn't Merckx do 29mph- for a hour-but in mexico City at altitude-? in the 1960's-well under 1 hp considering the altitude-decreased aero load.

That 1964 NASA graph-indicates world class athletes holding under 400 watts- maybe .5hp- AT 1 hour? Nothing like that 32mph almost 1 hp?
It seems to indicate 24mph at sea level is about average for first class athletes athletes? 1964
And 18mph is what a healthy man could hold fort one hour-1964?

DrkAngel

[h=1]Dutch cyclist sets world speed record[/h] [h=2]Dutch cyclist Sebastiaan Bowier sets a new world speed record for a bike as he rides at 83.13mph in Nevada, USA.[/h]Link - Human Powered Bike

[h=3]UCI hour record[/h]Link - 1 hour track distance

gsa103

Fabian Cancellera Tour of Flanders
6 hr, 22 min -- 285 W average

Peak power 1450 W

https://www.bikewichita.com/fabian-ca...flanders-2010/

DrkAngel

Actually, most any motor can push their peak power and efficiency point past the 50% of peak rpm point ...
Simple!
Just reduce the amperage of the controller.

It is not a function of any better quality motor, merely the equivalent of reduced throttle at lesser efficient speeds.
Sacrificing peak output for higher efficiency.

Kopsis

The problem is that human power and motor power are NOT necessarily linearly additive. With direct-drive motors, as you try to add speed with human power, you have to overcome both the normal additional drag on the bike AND the additional magnetic drag in the motor due to eddy currents and back EMF. Your speed increase numbers from 255W human input are wildly optimistic.