Power-gradient-weight-speed chart?

[Cugel]

After buying a new Fazua-equipped e-bike for myself, to match that ridden by the ladywife, we've been doing quite a lot of riding together with me either not putting the motor/battery module in mine or putting it in but not using it. We've been trying to find new power profiles for her e-bike that will match our power outputs and weights in a way that means we're going up the many hills at an equal speed for our respective personal sustainable maximum power outputs.

These outputs are about 125 watts for her and 220 watts for me. We can keep these levels up for the time it takes to climb even the longest hills, some of which take 20 minutes or more. Her motor allows her to add the 95 watt difference; or less or more (between a 0-250 watt range).

Working out what power profiles to give the ladywife's Fazua motor is complicated by me weighing 12st 12llbs and her weighing 8st 10llbs. (Note the fashionable use of imperial there)!

********

To find the best power profiles to set in her Fazua motor, we need a table/graph that shows the required wattage to push a range of weights (body + bike) up a range of gradients. She only uses her motor going up hills as we tend to go over 15.5mph on any flat (rare in West Wales) and down hill, so no motor involved requiring a power profile setting to "keep us equal".

My question: does anyone know of a table/graph/chart that shows power in wattage required for various rider+bike weights to go up various gradients at various speeds?

Cugel

[Jdsk]

My question: does anyone know of a table/graph/chart that shows power in wattage required for various rider+bike weights to go up various gradients at various speeds?

A recent discussion:
viewtopic.php?p=1696409#p1696409
included:



Jonathan

[Nearholmer]

Energy required to lift a mass a given height is mass x height x gravitational acceleration, then by using the time taken to achieve that (a function of speed when cycling up a hill), you can calculate the power.

You will then need to add in the power consumed by various losses: tyres on surface, bearing and transmission friction, windage etc.

Which isn't, I'm afraid, a table, or a set of curves, but it is a rough recipe for making one.

[Jdsk]

Energy required to lift a mass a given height is mass x height x gravitational acceleration, then by using the time taken to achieve that (a function of speed when cycling up a hill), you can calculate the power.

You will then need to add in the power consumed by various losses: tyres on surface, bearing and transmission friction, windage etc.

Which isn't, I'm afraid, a table, or a set of curves, but it is a rough recipe for making one.

And there are lots of online calculators using the recipe.

Jonathan

PS: What a pleasure to read an accurate description of the physics. Thankyou.

[axel_knutt]

My question: does anyone know of a table/graph/chart that shows power in wattage required for various rider+bike weights to go up various gradients at various speeds?

A recent discussion:
viewtopic.php?p=1696409#p1696409
included:



Jonathan

I clipped that plot down to just the relevant uphill section for the previous thread. Downhill, when gravity is already giving you several kilowatts, you can see how little difference a few watts from your legs makes against the cube law of wind resistance:

[Cugel]

Energy required to lift a mass a given height is mass x height x gravitational acceleration, then by using the time taken to achieve that (a function of speed when cycling up a hill), you can calculate the power.

You will then need to add in the power consumed by various losses: tyres on surface, bearing and transmission friction, windage etc.

Which isn't, I'm afraid, a table, or a set of curves, but it is a rough recipe for making one.

Although I have A-levels in maths (and also what was then called higher maths) it was 55 years ago and I'm afraid I took the easy option of studying philosophy at uni. Far easier to woffle on than get one's head around them maths, man!

I did look at those basic calculations you mention, though. The difficulty comes with some of those extra factors, particularly "windage", which operate in a non-linear fashion so that the graph calculated with that and perhaps other factors becomes a complex curve. I was hoping for a simplified graph/table that nevertheless took in some of those extra non-linear factors, at least to a degree that gives a more accurate if not ultimately accurate picture. Jonathan's graph looks to be a decent thing to start with.

************
The Fazua software provides two main variables for setting it's three power profiles (pootling, going harder and "fool gaz"). The first variable sets the slope for your own power input, between none and a value at which the motor gives the maximum power for that particular power profile. The second variable is the slope of the added motor power, from none to the maximum it will give for that profile once you reach the max for the first (rider power) input.

For example, the ladywife's pootle mode has a maximum motor output of 70watts, which is given when she, the cyclist, outputs 125 watts herself, with proportionate amounts (cyclist to motor power) below those values.

What I'm after is finding a pootle profile for the ladywife such that I can only just keep up with her when going uphill, unpowered, when she is in pootle-power mode.

I'm also looking for two profiles (one for my bike and one for hers) such that a pootle mode for me will match her uphill speed when she's in "going harder" power mode. E.g. I get 70 watts added and she gets 180 watts added, once we're outputting our own-body sustainable maximum power outputs. This means we both still have to try hard but we go up hills faster, which shortens the climbing time making more time for the rest of the ride.

That is, more miles for the same effort, courtesy of the Fazua motors.

I confess that going up some 300 metre climb hard but with the motor adding speed actually motivates me to try even harder than I would without a motor, since I won't have to ride eyeballs-out for nearly as long.

Cugel

[Jdsk]

Excellent, axel_knutt.

Can you also enter different masses to run those for Cugel's wife?

Thanks

Jonathan

Edited: Crossed with Cugel's.

[Jdsk]

Jonathan's graph looks to be a decent thing to start with.

Ahem... unwarranted praise!

: - )

Jonathan

[Cugel]

My question: does anyone know of a table/graph/chart that shows power in wattage required for various rider+bike weights to go up various gradients at various speeds?

A recent discussion:
viewtopic.php?p=1696409#p1696409
included:



Jonathan

I clipped that plot down to just the relevant uphill section for the previous thread. Downhill, when gravity is already giving you several kilowatts, you can see how little difference a few watts from your legs makes against the cube law of wind resistance:
S&G70.png
S&G.png
S&G120.png

I've tried so many times to convince club mates of old not to pedal down fast downhills but to tuck in their parts, bite the handlebars and go even faster, with no whirring legs and out-thrust elbows to muck up the air flow and actually slow them down as they pedal. Would they listen? No! They wanted an excuse to have an 11 sprocket and pedalling downhill was it!

When they eventually caught me up at the bottom, I would (once again) point to my biggest gear of 52 X15. They preferred the alternative fact that an 11 sprocket should make you go faster so I must somehow have one hidden about my person.

The power of the advert, eh, especially when it contains some macho stuff.

Cugel