How many watts is a good push worth?

The other day as I commuted home a stranger gave me a helpful push as I approached the top of a steep hill. It was wonderful, and I immediately wondered if this is what an e-bike boost would be like.

Is there some way to calculate how many equivalent watts a nice push produces? Very curious to know if it's on the low end (20 or so) or the high end (200 or so).

• You can calculate power as force * speed. Perhaps you could estimate the force by lying down and putting weights on your back that feel similar to the push, and multiply that by your speed.
– bdsl
Feb 1 '16 at 20:01
• Although a decent push will give you a physical boost a major benefit is likely to be the encouragement it gives you. The feeling that you can do it, and that if you don't you'll be letting someone else down after they helped you is quite powerful. There's some pretty strong evidence that you've got quite a lot in reserve when you're exhausted. Feb 2 '16 at 8:41
• "watt" are you talking about? Actually as a "side" comment, when I ride up over a bridge in my lowest gear (about 22 gear inches), my speed is only about 4 MPH but if I grab the railing with my hand and tug on it multiple times, I can get that up to about 6 MPH without pedaling any harder so there is power in my upper body being wasted on a regular bike only having foot cranks. I don't know the exact answer to your question but if I can go from 4 to 6 MPH using a boost from my 1 hand/arm and I am pedaling with about 100 watts, then I could think my arm is adding another 50 watts or so. Feb 6 '16 at 18:01
• We have quite a lot in reserve? Not me. I played like 54+ holes of golf one day (all day) walking on a hilly course and the next day I felt like every cell in my body was depleted of energy. However after resting and trying again maybe a week or so later, I was able to do similar but with less recovery time and not feeling so depleted after playing. Feb 6 '16 at 18:12

As others has said P = F X V

Lets say it felt 10 KG - under the force of gravity that is 98 newtons - lets just round up to to 100 N

Let say you were doing 15 kmh

100 N 15 km/h * 1 h/3600 sec * 1000/1k = 100 * 15 / 3.6 = 41.67 watts

If if felt like about 10 KG and you were doing 15 kmh then about 40 watts

Something like Gruber power assist is 200 watts

The faster you're going the more power you get out of a given amount of force or "push". Ad bsdl says, power = force times speed, so the same force at a higher speed requires or provides more power.

Going slowly up a hill even quite a strong push doesn't cost much power. A 200W "push" at 10kph will take you up most road hills with little to no pedalling, since that's all the power that's required. A 200W push at 70kph on the flat is noticeable but only just, because 200W requires less force and the rider is already having to put out 500W or so to go that fast. The extra 40% power also has a reduced effect since air resistance goes up as the cube of speed. Adding means 1.4x as much power but the speed change is roughly 1.4^1/3 = 1.11, so you'd only go ~8kph faster or 78kph.

You can experiment with this if you are the one giving the push. The relationship between how fast you're going and how much effort your legs have to put in for a given push force is quite perceptible even at relatively low speeds. It's very easy at a moderate speed to push someone and find that you're going backwards relative to them quite dramatically, but without their speed changing much at all. They'll be saying "go on, push" or "that did nothing!" while you're sprinting frantically to catch back up to them.

• In your last para I reckon you can treat it as a zero-sum exchange of momentum: for riders of equal weight every unit speed you give the other rider you lose. The speed difference can't be too great or it would be more a case of ramming the other rider, so the pusher is almost bound to end up quite a bit slower than the pushee. I assume here that the pusher can't suddenly increase their effort after making contact, because riding one-handed close to another bike up hill (and with the turning force of pushing with a hand to one side) isn't a good time to really pound the pedals. Feb 2 '16 at 6:56
• I find that I do exactly that, though. Position my hand then massively increase effort while pushing, then trail off behind when I tire out. With a margin for "I'm right next to someone and I only have one hand on the bars", of course.
– Móż
Feb 2 '16 at 7:03
• OK. That's interesting. Do you approach with very little extra speed then? Feb 2 '16 at 8:43
• @ChrisH yes, otherwise it's too hard to get my hand position right. Much better to approach relatively slowly then power on and change gears as required once I've got a good, um, grip?
– Móż
Feb 2 '16 at 9:07

I had a 400W motor for a while, and that felt like a good solid continuous shove.

Given the other rider is also going up the same hill, they have to keep powering themselves too, so anything they give you is in addition to what they need to keep pace.

It doesn't take a lot though - a push can be enough to take the edge off your muscles for a moment.

So I'd guesstimate somewhere between 20 and 100 W, probably in the middle.

TBH I'd be more worried about random strange cyclists coming close enough to push me, and if I was offering the push that someone would take it the wrong way. I mean - where do you push? Their arse is probably convenient, but you're gonna get yelled at. Saddle would be a second best, or pushing their shoulder could put them off balance.

It would be different if you know the other rider.

• I push the girly sometimes, but I know we normally ride fast enough that I put in 200W or more, but only for 10s or so to get her back up to a decent speed.
– Móż
Feb 1 '16 at 23:40
• @Mσᶎ yes, but she knows you and you know her. Some random cyclist may see it as an invasion of their space.
– Criggie
Feb 3 '16 at 18:35
• yes, I'd never do that to some random cyclist I happened to be overtaking.
– Móż
Feb 3 '16 at 21:41