when you ride fixed and take most of the slack out of the chain, just going over a bump can cause the tension in the chain to be momentarily incredibly high. [There is no such thing as a perfectly flat catenary, and the tension becomes asymptotic as you approach flatness; a modest vertical load on a nearly-flat chain run can cause a tension increase in the chain that is a hundred times higher.] By contrast going over a bump on a geared biike just causes the derailleur to deflect slightly; no real increase in chain tension occurs.
In addition when you ride fixed you may create tensions in the chain that are several times higher than normal, because if you don't, you won't get up steep hills. By contrast on a geared bike you are unlikely to have to push that hard on the pedals; most folk just change gear instead.
The peak loads when riding fixed come from going over a bump at the same time as giving it what for.
The friction between two surfaces that are clamped varies from about 0.1 x the clamping load to about 1.0 x the clamping load, depending on the nature of the surfaces.
Note that to start a QR wheel moving (with the lever on the left and the QR nut on the right), all you need is for the RH locknut to start sliding; the threaded part of the QR skewer may be clear of the hollow axle and the axle may be able to move slightly without the QR nut also sliding. If the QR nut is impeding movement, it won't be able to exert a very high force to stop the wheel, because it isn't that difficult to bend a length of M5 x 0.8mm studding.
By contrast when you tighten a (good) track nut properly, both the track nut and the hub locknut have to slide past the dropout before the wheel will start to move. This means that even at the same clamping load, a nutted axle is less likely to move.
The clamping loads also vary; roughly (estimated in skewers by the clearance change in cup and cone bearings)
- external cam QR = up to ~ 500kgf
- internal cam QR = up to ~ 500- 750kgf
- screw type 'security skewer' = up to ~1000kgf
- breaking load of QR skewer between ~750kgf and ~1250kgf depending on quality of skewer and loading.
- axle with track nuts (3/8" or 10mm thread) up to ~ 2500 kgf.
FWIW if you are a strong rider, horizontal aluminium dropouts are likely to be a problem; unless they have steel facings they will very likely just get chewed up, even with gears. Without gears you are well advised to use a pretty solid chain tug. I used to break QR skewers on geared bikes (with horizontal steel dropouts) trying to get them tight enough that I definitely wasn't going to pull the wheel over. In the end I had to use the best quality QR skewers and had to be sure to use new, textured/ridged locknuts on the RHS of the hub. When riding fixed the built-in washer on many track nuts just wasn't strong enough and would deform. If they were less tight than that I'd risk pulling the wheel over.
Note that the wheel adjusters in horizontal dropouts allow a geared rear axle to return to the same spot each time and that is usually where the dropout will best accommodate the locknut positively; quite a lot of QR hubs had a ridge on the locknuts which made a corresponding groove in the face of the dropout. However when running fixed or SS, the wheel never goes back in the same place twice, so the surfaces never get to mate in the same way.
I've never been able to reliably ride SS or fixed using a wheel with a QR skewer, and nor has anyone else I've known who has been a strong/quick rider. Riders with 'explosive power' can (briefly) be pushing four or five times harder on the pedals even than folk who are really quick over a distance.
By all means try using fixed gear with a QR skewer if you must, but IME it is bad practice and is very likely to lead to problems.
cheers