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In my neck of the woods there are some mountain descents that are pretty substantial: say 600 meters vertically averaging 7% grade, with lots of curves and other obstacles like potholes. Typically the surface is reasonable-quality asphalt; I have a touring bike.

I’m curious if there are techniques or gadgets to moderate my speed, in order to lessen the need for braking (e.g., in a car one can downshift).

As a back-of-the-envelope, computation, consider a 110kg rider/bicycle system coasting down a 7% grade at 50km/hour, or about 13 meters/second. Due to the grade, for every horizontal 13m, s/he descends 0.91m vertically; hence, every second, the potential energy of a 110kg mass dropping 0.91m is added to the bike & rider system and must be removed in order to not accelerate. That potential energy (U=mgh) is roughly 980 joules; i.e., the cyclist must dissipate about 1kW in order to not accelerate.

This surprises me; it seems like a lot of energy to be dumping into the environment. But it's on par with what can be produced by racers to reach similar speeds on the flat.

What I don't know how to compute is how much energy is consumed by air drag, mechanical friction in the bicycle, rolling resistance, etc., to know really what extra a slowing device would need to consume.

One thing I thought of was a dynamo hub; but those seem to consume less than 5 watts, which would make no real difference.

(I should add that I know I shouldn't brake continuously all the way down. My question is about whether there are additional things I can do or add to the bike to bleed off speed.)

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Is it off-road (downhill) or road (asphalt)? –  heltonbiker Jun 17 '12 at 19:46
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It's asphalt, and I'm on a touring frame (i.e., more or less a road bike). –  Reid Jun 17 '12 at 21:48
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Out of pure curiosity, why are you trying to find a solution for something your brakes should do just fine at? –  Jack M. Jun 18 '12 at 1:30
    
I'm pretty sure that mountain descents without braking are not possible. –  user313 Jun 18 '12 at 21:12
    
@Jack, brakes aren’t “just fine”. It’s tedious to keep braking on a 1-2,000 foot descent. They do work, but it would be a much more pleasant ride if my terminal velocity were more reasonable. I’m not in it for the adrenaline; others may be. –  Reid Jul 4 '12 at 17:32
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8 Answers 8

up vote 14 down vote accepted

There are two parts to your question, and two answers. The first part of your question is whether there are devices to moderate speed on descents. This is a common issue with tandem bikes (and occasionally with bikes designed for loaded touring). Many tandem-specific rear hubs have a threaded left side onto which can be mounted a "drag brake." Typically a drum brake, they can be adjusted for a slight amount of drag; the rim brakes are retained as the primary brake for stopping. The advantage of the drum brake is that it's away from the rim (since excessive heating at the rim can have dire consequences for tube or tire) and they have a high heat capacity. Although no longer manufactured, the venerable and venerated Arai Tandem Drum brake was an example of this.

Your second question is about how one would estimate the drag demand on a bicycle. This is a well-understood, though perhaps less well-known, problem, and is discussed in Section 2 of Wilson and Papadopoulos' Bicycling Science. As you surmised, the potential energy component has to be offset by drag elsewhere: either by aero drag, braking, or rolling resistance. Terminal velocity is achieved at the point where the potential energy loss exactly balances the drag forces generated elsewhere. The coefficient of rolling resistance (Crr) happens to scale exactly like slope, so a change in slope of 1% is exactly like a change in the Crr of .01. Sadly, for this purpose, you won't much be able to rely on Crr for appreciable extra drag -- commonly, Crr ranges from about .004 to perhaps .01. Thus, although in a theoretical sense you must take rolling resistance into account, in a practical sense it dissipates too little energy to matter. Deflating tires to increase Crr on a twisty descent is not just insufficient, it's a bad idea.

Aero drag is more easily manipulable but is also limited in efficacy. Drag area (typically denoted by the product of the frontal surface area, A, and the coefficient of aerodynamic drag, Cd) for a typical cyclist on a typical road bike will range from around .3 sq meters (roughly, 3 sq. ft) up to perhaps .5 sq meters or higher. Aerodynamic drag force varies with the square of airspeed (since the force varies with the square of airspeed, the power demanded to overcome that force varies with the cube of speed) so sitting up, unzipping a jacket, and widening your arms and legs can add some CdA; however, rarely more than ~ .2 sq meters.

That leaves braking, i.e., the conversion of potential energy via kinetic means into heat, and the place for a drag brake as described above.

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Thanks! Do you know of any online resources that could help me estimate drag in watts based on surface area? I found some resources (e.g., my.execpc.com/~culp/rockets/descent.html) that offer calculations giving a drag force, but I don't know how to convert that to watts. Or am I framing the problem incorrectly? –  Reid Jun 17 '12 at 22:09
    
Well, the short answer to your question is how to convert drag force into power, and that's simple. Convert the drag force into Newtons, then multiply by speed in meters/sec. A watt is a Newton-meter/sec, so if you're traveling at 10 m/s and experiencing, say, 3 kg of drag "force", you'll just convert to Newtons then multiply by speed. That's 3 * 9.8 m/sec^2 * 10 m/s = ~ 300 watts. The longer question is how to estimate drag area on a bike. The answer is long (and I have fewer than 10 characters of explanation left) so that probably deserves its own question. Ask it and I'll answer. –  R. Chung Jun 17 '12 at 23:01
    
@Reid, Basically, ask something like this: "I want to estimate either the amount of drag force when coasting down a hill at a certain speed, or the amount of power needed to ride on the flat or up a hill at a certain speed. All of the online calculators either assume coefficients of rolling resistance or aerodynamic drag or assume that I have estimates for them. How do they make those assumptions, or how can I make those estimates myself?" –  R. Chung Jun 18 '12 at 1:21
    
done (bicycles.stackexchange.com/questions/9938); thanks for suggesting it! –  Reid Jun 18 '12 at 3:03
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You don't say what type of bike you are on, but there are some simple things that will help.

  1. Sitting up and getting your body as wide as possible will add a significant amount of drag. You can also wear a jacket and unzip it 7/8 so it catches wind.
  2. Slightly lower your tire pressure. Don't go so low that you lose stability, but the rolling resistance between 105psi and 120psi will make a difference
  3. Find high rolling resistance tires. There are a number of sources for this data based on your bike type.
  4. Not directly related, but make sure you use appropriate brake pads and rims/rotors. Some do better with long decants than others.

There are also the obvious comments like learn to descend at speed or switch to a slower bike.

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Regarding “learning to descend at speed”, the natural equilibrium on these descents is 40-50 MPH. The posted speed limit is 25 MPH, which is quite reasonable given the tight curves. I don't have any desire to blast through such curves, which are atop cliffs and are often the steepest parts of the ride. Thus, the basic point is that I'd rather descend more slowly overall, rather then accelerating to 50MPH on the straights and having to brake sharply before entering curves. (Similarly, the routes are so steep that a “slower” bike would have little practical effect.) –  Reid Jun 17 '12 at 21:52
    
Stefan provided a good answer. Seriously? You want to add stuff to your bike...and make it harder to get up? –  user313 Jun 18 '12 at 20:53
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Anyway, why would I add stuff to my bike to slow me down on the downhills; when it would also slow me down everywhere else? –  user313 Jun 18 '12 at 21:26
    
Regarding point #2 about lowering tire pressure from 120 psi to 105psi: measurements on smooth surfaces show that Crr decreases as pressure increases, so you're right: lowering pressure will increase rolling resistance. The conundrum is that on not-quite-so-smooth surfaces, measurements show a "V"-shaped relationship between pressure and Crr so that sometimes lowering pressure actually reduces Crr. Interestingly, the "V" appears not to be symmetric, so being a bit over "optimal" pressure increases Crr more than being a bit under. Unfortunately, "optimal" depends on the road surface. –  R. Chung Jun 21 '12 at 17:55
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Some electric bicycles have regenerative braking. That's the only thing I can think of that comes close to answering your question.

Theoretically, you could use something like a parachute to slow down, but this would create way too many problems (side winds, chute getting tangled in the back wheel, having to retract the chute when you don't need it anymore, etc).

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If you're asking for a DEVICE to control the speed, some tandems (two-seat bikes) have a dedicated brake system called "Drag Brake". From the Sheldon Brown page on tandem brakes:

Friction Control Drag Brake

The most common, and most satisfactory system is to set up the rim brakes, one to each conventional brake lever, and operate the hub brake by a friction-type derailer shifter. This may be a "Barcon", a mountainbike-type thumb shifer, or a Sun Tour Command Shifter.

A friction-type shifter allows the captain to set the hub brake to apply the desired amount of drag, even once he or she has let go of the hub brake control. the captain then uses both hands on the rim brakes to modulate the bike's speed, and to stop if it becomes necessary.

While the most straightforward strategy would be to use a rear wheel with rim + hub brake, one for the handlebar lever and other to the friction-shifter, there are some dedicated hubs to use as drag brakes (although they are most probably cumbersome and difficult to find). One model I found on Google is the Arai Drum Brake (out of production).

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Could a mechanical disk brake and thumbshifter work to accomplish a friction brake? I doubt you'd want indexing shifters, but a non indexing one would allow you to set a 'constant' braking force on the disk brake, while still reserving the rim brakes / front disk brake for stopping... –  Ehryk Jun 20 '12 at 0:56
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@Reid - would this solution be something that you'd be interested in? Or were you limiting it to off-the-shelf solutions? –  Ehryk Jun 20 '12 at 0:57
    
@Ehryk The idea is to adapt friction shifter to activate the second brake. The still has the normal brakes and the normal shifters. When you go along a downhill, you twist the friction shifter to the desired braking force and it keeps applying that constant force (since the lever stays in position), while the hands are free to do anything else, including brake even more with the regular brakes, or changing gears with the regular shifting system. –  heltonbiker Jun 20 '12 at 13:38
    
I understand that - what I'm asking is if a modern disc brake (mechanical or hydraulic) can serve that purpose, since the drum models are not produced any longer? Then the rim brakes or rear rim / front disc would be free to add stopping power. –  Ehryk Jun 20 '12 at 18:13
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In motor vehicles, it is preferred for stopping power and rotational weight concerns; however drums are preferred in large semi trucks (non steer wheels) because of much better heat dissipation. You can't 'ride' disc brakes for nearly as long as you can drums before they warp and/or boil the hydraulic fluid. They may be appropriate for bicycles, however. –  Ehryk Jun 20 '12 at 21:00
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I've never heard of a ready-made device to do what you want. The only thing I can think of is to get the fan or magnetic resistance device from a training stand or rollers and somehow attach it in a way that it can be switched on and off. Or even better would be to get a rig such as used in some exercise bikes where there is an aluminum flywheel with an electromagnet arranged next to it, such that resistance increases as the magnetic field increases. (In theory a deep aluminum rim could be used instead of the flywheel.)

But you'd have to salvage parts from somewhere to do any of these, and then do some machine shop work.

Otherwise probably the best solution in your case is a bike with disk brakes.

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You could build or buy a drogue chute. It need not weigh very much, being less than a square metre of ripstop nylon and a couple of metres of thin cord. It may even be legal to do so, depending on how your country writes the "no sail powered vehicle" laws (or whether such a law exists). I'd be inclined to make it tear away by attaching it to my body with velcro.

I've done the opposite, and used a small sunshade/tent door as a sail when I had a strong tail wind and I was going uphill on my touring bike. It worked disturbingly well, in that I had to move the main attachment from my backpack waist belt to the seatpost as it was threatening to catapult me over the handlebars (the bike was quite heavy).

As a brake I suggest a cross-style drag chute as they're easy to make and more stable than a round or rectangular chute (rectangles are more controllable but unless you're used to parasailing or kite surfing the learning curve is steep).

The main problem I can see is that mountains often have wind, and specifically the wind can vary dramatically over short distances. For example, if you come out round a ridge you may move from still air behind the ridge to compressed wind on the exposed face, and the change in drag from a chute will be dramatic. In that case you have to decide whether you want to drop the chute onto the windscreen of the car that's following you, or slow suddenly in front of it. Either could be embarrassing.

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You could always get a fixed gear and use your legs to slow you down. Getting back up the mountain would present a completely different problem though. Although with the right gear ratio it would probably be possible to go both up and down the mountain on a fixed gear.

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I'd wager that any gear reasonable for ascent would be crazy on the descent. I'm happy to go 30 MPH; I just don't want to do 50. –  Reid Jun 17 '12 at 21:46
    
I was thinking it would be nice if there was a dual-drive train bike, so you could control your speed on the descent with the fixed gear component, plus use gears when not going down the hills. So I figured either it's impossible due to mechanics, or somebody has already built one. And after a little Googling I found this (sheldonbrown.com/bichain-fixed-free.html). Reading into it, it says it would be possible to build it with a derailleur system on one side, and fixed gear on the other side. Definitely interesting, although probably way more complicated than what you're looking for. –  Kibbee Jun 18 '12 at 1:19
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I can do 30mph fixed with no problems, and it's not a particularly high gear - if you find a gear that will get you up, you just need to practise spinning on the way down (note that you can just let the pedals pull your feet round if you relax, and you get a similar engine-braking effect to downshifting in a car). Or, of course, stop at the top and swap sprockets ... –  Useless Jun 19 '12 at 13:20
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Maybe use disk brakes, not rim brakes, if heating is a problem.

I'm used to the idea that people put about 1 KW into the environment just by existing; I'm not sure what the problem is, with losing one extra KW when descending.

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I believe base metabolism is more like 100 watts, but I haven't looked it up. –  Reid Jul 4 '12 at 17:36
    
@Reid - you seem to be right: per engineeringtoolbox.com/met-metabolic-rate-d_733.html it ranges from 100 watts when seated, to 500 watts when bicycling, to 900 watts when running. –  ChrisW Jul 5 '12 at 17:28
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