What are similarities between cyclists pedaling to develop power and an engine?

[RPS]

As a cyclists and a fan of automotive engineering I find it interesting that there seem to be similarities between engines and bike riders when it comes to producing power. Not to say there is direct correlation or anything like that, but the similarities are intriguing considering we have almost nothing in common – except we both burn fuel with oxygen to do work.

For starters, both cyclists and engines seem to have a sweet spot for efficiency, right? That “perfect” level of power and cadence that gets us down the road with minimal drain. Also like engines we develop highest power at higher-than-normal RPM, but we do so at reduced efficiency. For an all out sprint (requiring lots of power) we need higher RPM, but we wouldn’t ride a century at that cadence, would we? It’d be highly inefficient ATMO. Another similarity is how we prefer to climb at a much lower cadence which is analogous to running an engine at near peak torque.

Many times we hear cyclists describe efficiency as a function of cadence (by saying something like “I’m most efficient at 80 to 90 RPM”). Maybe so, but isn’t that at only one particular load/power level? Maybe that cadence works best for a time trial or when cruising down the road at 20 MPH, but isn’t it common sense that if we were riding next to a small child and only producing 25 watts that we’d pedal much slower than our preferred 80 RPM or whatever is “normal” for us? We mostly discuss pedaling efficiency as a function of cadence, but like engines shouldn’t we also consider the effect load has on the bigger picture?

My question is this: What would performance maps look like for cyclists? Would they be reduced to single lines or curves representing efficiency as a function of cadence as is normally reported, or would they likely be more involved? Any thoughts or ideas?


P.S. – For this purpose let’s assume we’ve already learned how to pedal as efficiently as we are going to get given predetermined conditions.

[RPS]

For those who don’t know what one looks like, below is a performance map for an older US V-6. Note that sweet spot for efficiency; and that it doesn’t coincide with either max power or max load. Is it possible we are different yet similar in that it’s not a simple line or curve dependent solely on cadence?

[palincss]

The most dramatic difference is the very narrow RPM band of the human cyclist vs the automobile engine, from somewhere around 25-30 RPM at the very low end on up to at very most 250 RPM or so, if some of the fixed gear fans I've read on lists can be credited. That's a range of perhaps 225 RPM, compared with roughly 4000-5000 RPM range (idle at just under 1000 to redline at 5000-6000, give or take a little) -- roughly 1/20 the range.

[Brian Smith]

There's no sensation that correllates with maximum efficiency.
That means that what a rider might imagine based on sensations is their cadence of maximum efficiency is just imagination.

A sensitive motor vehicle operator can find the meat of a motor's torque curve, but the point of highest available torque is almost never the engine's speed of maximum power.

The condition of a motor's maximum power is also not the condition of the motor's maximum fuel efficiency. Time trial endurance is not about maximum power, it's about maximum efficiency. Once you toss additional riders into the mix, strategy and tactics play at least as much part as biomechanical stuff that one might possibly imagine has analogues in the performance of engines.

[Brian Smith]

The most dramatic difference is the very narrow RPM band of the human cyclist vs the automobile engine, from somewhere around 25-30 RPM at the very low end on up to at very most 250 RPM or so, if some of the fixed gear fans I've read on lists can be credited. That's a range of perhaps 225 RPM, compared with roughly 4000-5000 RPM range (idle at just under 1000 to redline at 5000-6000, give or take a little) -- roughly 1/20 the range.

Contrariwise, 6000rpm/800rpm is pretty close to 200rpm/25rpm.
The difference in each rev. range is about 750%.

[Tobias]

My question is this: What would performance maps look like for cyclists? Would they be reduced to single lines or curves representing efficiency as a function of cadence as is normally reported, or would they likely be more involved? Any thoughts or ideas?I certainly hope this isn’t an April Fool’s joke in waiting. ;)

I’ve mostly seen efficiency data for cyclists expressed as a function of cadence while holding either torque or power constant, and a few times as a function of percent power (i.e. – load) holding cadence fixed, but I’ve never seen both combined into a map that would resemble the one above. I have to admit it would be interesting and very useful to map a rider over a wide range like that although it would be difficult to conduct the tests because riders would fatigue before the data could be collected. And if testing was done over multiple days it may skew the results due to variations in performance from day to day – something that wouldn’t happen to a machine.

From my recollection of the data (will try to find the link) the results varied by both cadence and load, so if combined they would not follow a single line or curve. I’d also agree that as the load approaches zero, the efficiency has to go to zero. I’m assuming that if a rider spins at 80 RPM with zero load and therefore produces zero power, his efficiency would be zero. So I’d have to conclude that load plays a major factor.

[Tobias]

Contrariwise, 6000rpm/800rpm is pretty close to 200rpm/25rpm.
The difference in each rev. range is about 750%.That's also the way I would look at it; as a percent.

Although I wouldn't use 200 RPM for cyclist since that is not a normal range. It can be done, but that's like saying engines can spin 12,000 RPM. Not very useful information in normal context.

Personally I'd pick numbers like 120 RPM as a "normal" high end for most riders, 80 RPM as a "normal" range for cruising, and maybe 40 RPM as a low end at which pedaling becomes too inefficient.

From my perspective an RPM range of about 3 to 1 probably covers over 90 percent of normal use for either rider or typical auto engine. That useful range ratio would be another similarity.

[RPS]

There's no sensation that correllates with maximum efficiency. :confused: What about being more or less out of breath while trying to maintain a constant speed (i.e. -- level of power)? Don’t you think you’d learn over time what cadence works best for you for a given effort?

If I ride at 20 MPH at 80 RPM I feel more aerobically comfortable than if I spin 120 RPM. Isn't that a sensation of greater efficiency?

[Tobias]

:confused: What about being more or less out of breath while trying to maintain a constant speed (i.e. -- level of power)?We can also depend on data from a heart rate monitor instead of "sensation", although that too is important. I'd assume the lowest heart rate for a given power would suggest higher efficiency.

[Louis]

Certainly one of the major differences is that the engine will perform essentially in the same manner, from minute 5 all the way through hour 99999.

Humans "wear out" very quickly (except for Jure Robic). Calculating efficiency for humans it therefore much more complicated, if not impossible.

[RPS]

Calculating efficiency for humans it therefore much more complicated, if not impossible.Louis, I agree that it would be more difficult to obtain the data, but I think it would help many of us better understand how cyclists can best produce power at different intensity levels; which could lead to smarter riding by optimizing our potential. Even if the data couldn’t be collected with “precision”, it would be better than not having it at all.

I have no doubt that maps for cyclists would all be of considerably different magnitudes (speed, torque, power, efficiency), but I’d expect the general shape of the maps to be very similar between individuals regardless of their ability. If we compare the performance maps of two completely different engines (say a high-performance V-8 versus a small Prius 4-cylinder) the overall general shape of the maps are very similar.

Is it not reasonable to expect different riders to follow similar trends?



BTW, I’m not sure performance maps haven’t already been done for cyclists; I’ve just never seen one and doubt it has been done. If anyone has I’d love to see a link.

[Ti Designs]

Let's start with the differences. The engine is a simple single dimention piston which uses thermal expansion to drive a crankshaft. By comparison a rider on a bike is complex, using four muscle groups and two pivots (I'm gonna ignore the ankle here) to drive the crank. There are ways for the rider to engage or relax muscles which changes the whole pedal stroke if they know what they're doing. This gives a good rider the ability to match the efficient cadence with the job at hand. A rider can stand on the pedals and use their whole upper body weight on the pedals, which is an efficient way of getting up a steep hill, but a poor way of adding energy to a system like going down a hill. Even the fueling systems are different. When the human body runs out of oxygen it switches to another system for short term use. Not many car engines have such smart management.

I've never been one to claim that humans have one efficient range - it's all about how you pedal the bike. Come to think of it, when I built my race car motor I threw out that assumption as well. My engine is a 1.6 Liter turbo+NOS with a lowered compression ratio to handle boost. That means at lower RPMs it should have nothing for torque, which is very bad for an autocross car. I designed a nitrous system that expands to a gas, thus letting me use stage 1 almost off idle - torque in a bottle. As the engine revs the ECU looks at all the normal parameters (manifold pressure, RPM, temp...) while another controller looks at RPM and throttle position to alter the ignition timing. With a turbo you have two possible cases, advance the timing for more power, retard the timing to spool the turbo quicker. Knowing the throttle position tells the ECU what the driver is asking for, adding nitrous (stage 2) replaces on-demand boost. At the top end detonation (ignition before TDC) is a problem. Octane is all about detonation resistance, as heat of compression rises you need a higher octane number. Problem - 93 is about all you get out of a pump. Part of fuel enrichment is cooling, my engine uses water injection at the intercooler for that (I shatter a lot of O2 sensors that way). For octane boost, propane has an octane number that's off the charts (would be something like 110), so when the knock sensor starts to notice detonation the system adds propane to the fuel/air mix. You can start to see how complex engine management can get, with different systems turning or or shutting down different things. My ECU knows what gear I'm in and what direction the wheels are pointed - adding nitrous when in 1st gear or when the CV joints are beyond 20 degrees would be a mistake...


So let's talk about how the two are similar(in ways you probably never thought of). Timing - it's all about the timing. If you were to take the spark plug wires off and put them back in random order the engine wouldn't run very well. That's kinda how most new riders (and some not so new riders) pedal the bike. My best example is firing the quad when the pedal is at 3:00 - pushing 90 degrees from the direction of travel of the pedal. When I teach my pedal stroke class I have riders work on one muscle group at a time, only firing that muscle where it can add power. The two muscle groups that take the most effort for most are the quads kicking over the top and the hamstrings pulling across the bottom. This is similar to advancing the spark timing as the RPMs rise. When they first start, I tell them the quads kick from 11:00 to 2:00 - have to shut down the quads when there's no longer a forward component to the pedal stroke. Their brains get a picture of where they need to fire the quads, but what really happens is they start late and end late. Flame propogation in an engine and muscle fiber recruitment in a rider works about the same, it's not instant. They have to reprogram themselves to start sooner then their senses are telling them.


The other similarity between an engine and a rider is after a winter of pushing heavy weights at the gym, my ass weighs about the same as a large block V8...

[RPS]

The other similarity between an engine and a rider is after a winter of pushing heavy weights at the gym, my ass weighs about the same as a large block V8...Aluminum or cast iron?

[Lifelover]

Efficiency for a internal combustion motor or for us is only indirectly related to RPM.

It much more complicated than that and is directly related to the fuel delivery system. And more specifically to the fuel delivery system's capablilty to quickly adjust to change in demand.

[Tobias]

From an old article/study I found on best cadence. Over ten years old but the trends should still hold.

Figure 1: The gross efficiency of cycling at 60, 80, and 100 rpm at various power outputs are expressed as a percentage of VO2max Note that gross efficiency at 100 rpm increases as power output increases so that at 70%, 80% and 90% VO2max the gross efficiencies at the three cadences are not significantly different. There is no disadvantage to pedaling at high cadences provided that power outputs are greater than 70% of an individual's maximal aerobic power.(Adapted from Sidossis et al Int I Sports Med,. 13(5), 407-41], 1992 .)

[Tobias]

Figure 3: Steady-state oxygen consumption in cyclists and trained noncyclists during cycling at 50, 65 , 80, 95, and 110 rpm at a power output of 200 VV Note that the cadence at which VO2 is minimized is significantly lower than the preferred cadence in each group. Despite many years of cycling experience, the cyclists had not adapted so that they minimized oxygen consumption at their preferred cadence. Also the preferred cadences of the trained noncyclists were the same as the cyclists. Therefore many year s of cycling training are not necessarily required to feel comfortable at high cadences. (Adapted from Marsh and Martin, Med. Sci. Sports Exerc., 25(11), 1269-127A 1993.)

[Tobias]

It appears that spinning very fast at low loads (claimed below 70%) is not very aerobically efficient. Makes sense to me based on personal experience.

Also makes sense that if one is limited by aerobic capacity prior to muscular fatigue -- as when climbing a tough hill with relatively fresh legs -- that a low cadence in the range of about 60 RPM gets the most out of limited oxygen supply. Trying to climb at 100 RPM or other fast cadence would have little short-term advantage.

[RPS]

It appears that spinning very fast at low loads (claimed below 70%) is not very aerobically efficient. Makes sense to me based on personal experience.Thanks; interesting data. Spinning under low load doesn't work for me very well either.

The format of the information is different, but could be recalculated to show it similar to a performance map. Also of interest is that when it mentions 70 percent it isn’t talking about 70 percent load as in torque supplied through pedals to crank arms (which is typically the “y” axis on performance maps), but rather 70 percent of max VO2.

The significance of this is that when pedaling at 100 RPM versus 60 RPM for a given oxygen consumption, much less force is being applied to the pedals in the first place. Therefore, taking a percent of that makes the “load” (as in average torque) even lower than it would first appear.

That too is not unlike an engine – very low torque production results in low efficiency (applies to all engines I've ever seen -- some more than others). That’s the main reason overdrive transmissions were developed to conserve fuel – they run the engine at a lower RPM and higher torque to get closer to its efficiency peak. It appears from this data that both trained and untrained cyclists have maximum efficiency below 70 RPM – lower than I would have expected. Unfortunately the data was collected at 200 watts and there is no way to know what would have happened at other power levels.

As a side note, one of the reasons a Prius gets great mileage is that by using a continuously variable transmission (CVT), they run the engine at near peak efficiency most of the time. I ran across this map for an earlier Prius (reportedly -- I have no way to confirm but looks right) some time back.

[Tobias]

Calculating efficiency for humans it therefore much more complicated, if not impossible.That was my first thought too, but I’m now thinking that it may not be that difficult to obtain good data.

With power, cadence, and heart rate monitors, most of the data can already be collected while out riding a standard bike. All that’s needed is lots of data storage and the right software to map the rider’s performance. Because fatigue could be an issue, data from multiple rides could be averaged out for better accuracy.

The only thing missing is a way to monitor oxygen consumption to estimate rider efficiency, but two things could be done to overcome that provided total accuracy is not needed. The rider could be tested in a lab so as to correlate heart rate with VO2 and then use that data to substitute VO2 for heart rate data (expensive and awkward process), or to keep it simple the map could be done with heart rate in place of efficiency. The latter is not only simpler but would indicate rider performance just as meaningfully to most of us. If I looked at my map and it predicted a set of conditions would result in a heart rate of 155, that would tell me more than if it said that my efficiency was 22 percent.

[Tobias]

As a side note, one of the reasons a Prius gets great mileage is that by using a continuously variable transmission (CVT), they run the engine at near peak efficiency most of the time. I ran across this map for an earlier Prius (reportedly -- I have no way to confirm but looks right) some time back.I can make out the lowest fuel consumption rate for the Prius at 230 grams per kilowatt-hour but can’t make it out for the older V6 engine. I’m curious what that number is and how old is that engine (to see improvements in technology over time).

Also, why the KW lines on the bottom left corner only? If constant power lines why not across the entire map? :confused:

I’m guessing these maps are crucial for engineers to calibrate electronically-controlled automatic transmissions to maximize fuel economy much the same as with a CVT. Having a computer making more objective decisions is probably one of the reasons automatics now get better MPG in some cases than manual transmissions.

What's next, combining rider mapping with electrical bike shifting to maximize performance? :rolleyes:

[RPS]

I can make out the lowest fuel consumption rate for the Prius at 230 grams per kilowatt-hour but can’t make it out for the older V6 engine. I’m curious what that number is and how old is that engine (to see improvements in technology over time).

Also, why the KW lines on the bottom left corner only? If constant power lines why not across the entire map? :confused: As I recall it’s based on a 80s Ford 2.7 liter V-6. The lowest specific fuel consumption rate (circle at about 2000 RPM and 140 Nm torque) is 260 grams/kW-hr (or about 0.42 pounds/horsepower-hour). The highest BSFC at the bottom is 410 g/kW-hr.

The Prius’ 235 is on the low side compared to others I’ve seen. Newer engines from Saturn or Mercedes for instance are rated at around 250 grams/kW-hr.

Regarding constant HP curves, I don’t know why they only overlaid three up to 10 KW and then stopped. I’ve seen many maps with HP curves overlaid over most of the data to make it easier to use the information. The VW TDI map below is an example. The Mercedes also, so maybe it’s a German thing. :rolleyes:

BTW, don’t get confused by the “y” axis on the VW TDI map. Torque is expressed as mean effective pressure; which is done to allow easier comparison of different size engines.