Jeremy... it's been 60+ years since I took high school physics, so I must confess that I didn't follow any of that.
![Smile :) :)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
(That is physics, right?)
I'm not sure what my friend weighs, but let's say 210lb. As for speed, it varies of course, but I'd say between 5-10mph. I'm 76. My friend is 77 and a life-long biker, with very strong legs. He's willing to push harder than I am.
Understood, but it's not as hard as it might look. The last formula I gave is all you need to get a ballpark estimate of the motor power you need to compensate for your extra total weight. And from various posts here, we now have the necessary data.
The short answer: At 6 mph up a 6% slope, about 17 W.
Showing my work
To end up with power in Watts, easiest to work in metric units. You are rider 1; your friend, rider 2. Technically, the "weights" you gave are actually masses, so I'll rewite the last formula to reflect that:
Pw1 -
Pw2 = (
M1 -
M 2)
g (s + Cr) Vg,
where
M is total (rider+bike+cargo) mass,
g is the acceleration of gravity,
s is your average slope,
Cr is your coefficient of rolling resistance, and
Vg, your average ground speed up the slope. All but the masses are the same for both of you.
Assuming the stated bike masses include all accessories and water,
M1 = 215 + 35 lb = 114 kg
M2 = 210 + 18 lb = 104 kg
M1 -
M2 = 114 - 104 = 10 kg
g = 9.81 m/s³
s = 6% / 100% = 0.06
Cr = 0.004
s +
Cr = 0.064
Vg = 6 mph = 2.7 m/s
Pw1 -
Pw2 = (10 kg) (9.81 m/s²) (0.064) (2.7 m/s) = 17 W
So 17 W is all you need from the Vado motor to compensate for your greater total weight at 6 mph up a 6% slope. At 10 mph up a 10% grade, the extra power would increase to 46 W.
Implications
One important lesson here: Small to moderate differences in weight and rolling resistance translate into pretty small differences in required power on slopes under 5% at speeds under 10 mph.
To be clear, an extra kg can become meaningful on very long rides at higher speeds over steeper terrain. But not so much on typical recreational rides. On the flat, an extra kg means very little at any speed. In that setting, your focus should be on reducing air resistance, not weight.
That said, an extra few kg can make a significant difference in
responsiveness — i.e., in acceleration, braking, leaning, steering, and jumping. If you want a really responsive ride, by all means, sweat every kg — especially your own. Otherwise, relax.