Speed to power calc on a 'basic' magnetic trainer

Question

I'm a dedicated non-MAMIL, and I enjoy riding indoors on a cheap-and-cheerful 14-speed (max tooth ratio 48->14) attached to a $70 basic trainer while watching the footy or listening to music. No wind, no hills, no roundabouts, no car drivers trying to 'door' me, no public shaming from needing to get off the bike to push when I 'gas out' on a hill - seems all upside to me.

My usual exercise protocol is 'steady state' for ~1hour at an average HR in the high-130s and a total cal burn of ~1000kcal, and twice a week I do an HIIT-style workout -

• ride until I get my HR to the low 140s (which only takes a few minutes at cadence ~85 in top gear with 'wine cask' resistance), then
• 8 x 30-sec maximal effort sprints with 90 sec rest in between.

During my sprints, cadence is 120 (min) to 131 (max) in top gear, and HR always gets to 170 on the second sprint - that's my theoretical max given my age (51) and RHR (58).

After the sprint set, I do another 20-40 minutes at a cadence/gear combination that ensures that my average HR for the entire workout is in the 135-140 range and my average cal burn is 15 kcal/min.

I set my trainer so that it takes a 5-litre cask of wine (which weighs ~5.2kg) to move the pedal from horizontal. (This bit is a key input later, I think).

I'm buying a Wahoo KickR shortly so I will have a fair dinkum speed and power meter and this question will be answered by technology!

Until then I am interested in the performance analytics that can be done with basic mathematics based on what I have now (Wahoo cadence kerjigger in my shoe, Mio Alpha HRM on my wrist, and known-knowns like wheel diameter, crank length, force required to move the pedal, and cog ratio).

By year 10 mathematics it appears that my minimum sprint speed (based on 680mm rear wheel diameter, 120rpm crank cadence and 48:14 ratio) sustainable for 30sec is ~51km/hr, with a peak of ~56km/hr (at 130rpm, only held for seconds - so not relevant).

Those seem inordinately high for a fat old indoor hack - but bear in mind there is no wind resistance, no drag, and to the extent that the 'wine cask' resistance mimics a slope I'm not actually having to move my bodyweight (104kg) or bike (12kg) up the slope.

So here's the question (finally): is there enough information there to estimate power?

We have:

• crank length 175mm;
• rear wheel diameter 680mm;
• cadence 120 rpm;
• gear ratio 48:14;
• mass required to move pedal from horizontal 5.2kg (with empty bike)

I am reasonably certain that my (and the bike's) weight - 104kg and 12 kg respectively - are irrelevant, except to the extent that when I get on the bike the mass required to move the pedal would increase slightly (probably not enough to really make a meaningful difference to the calcs).

Almost all the power formulae that I've found, use the rider+bike weight - which is pointless on a trainer. If I subtract my weight, then the power formulae return garbage (and are way out of whack with the caloric expenditure during the 'effort' sets).

Has anybody got any insight on this?

Answer 1

The short answer to your question is: no, there's not enough information.

In the main, the information you lack is about your particular trainer's resistance curve as it varies with roller speed. Each magnetic trainer has a particular "design curve" for its resistance, and you can see some examples here. As you can see, magnetically-braked trainers tend to have a "flatter" power curve than fluid or turbofan trainers. Different manufacturers will use different numbers of magnets and different thicknesses and materials for their rotor in their resistance units. Some magnetic units allow you to alter the distance to vary the resistance. And, each load generator typically has a way to dissipate heat so the load often varies even for the same roller speed when the unit is cool vs. warm. You can often see this by directing a fan at the load generator and noticing a change in resistance. In addition, as parts wear over time the load units and bearings can become misaligned.

You are (almost surely) correct that your total mass (you + bike) is irrelevant since for (almost) all basic magnetic trainers, the roller-to-tire contact is set by turning a knob to press one against the other. That roller-to-tire contact is the same whether you are on the bike or not. When you ride on the road, on the other hand, the road-to-tire contact is determined by your mass. As an aside, trainer rollers are typically about 3 to 4 inches in diameter so for a given total mass the roller deforms the tire more than it would on a regular road surface, so a Newton of force on a trainer roller imposes more rolling resistance than the same Newton of force on a road.

BTW, here is a way to check your "cask on pedal" method for calibrating rolling resistance: Adjust the tire-to-roller contact so that your 5.2kg weight just begins to move the rear tire in a 48-14 gear ratio, as you've been doing. Then, vary the gear ratio and find the pedal weight that will once again move the rear wheel. The ratio of mass to gear ratio ought to be constant.