Power calculation from torque 1

[BruceDiesel]

Hi All,

I hope this is the best forum for this question - because it is not directly related to electrical motors, but I believe this would be the best place to find the answer.

The problem I have actually relates to the calculation of power based on varying torque and angular velocity (on a bicycle of all places).

Background:
A power meter on a bicycle measures a cyclists power output by measuring torque (sampling it at around 70Hz and averaging those 70 samples) then multiplies this average by angular velicity derived from the rpm to provide a power reading once per second.

It is common that a cyclist experiences difficulty in achieving the same power outputs when riding on an indoor trainer (which uses a flywheel and applies a resistive load to the rear wheel) as apposed to riding outdoors.

My hypothesis is that the torque pattern changes between these two environments (do to the removal of the mass damping effect that the riders body mass provides) and that using an arithmetic mean to calculate the average torque per rotation is in fact not correct, and that the torque for the rotation should be calculated using a root-mean-square.

It's been 20 years since my undergraduate days so I'm dusting out the cobwebs

 

[DaveScott]

I was thinking that if the gearing is lower, then the change in flywheel speed is less, therefore the energy exchange is less from bike wheel to flywheel.

 

[cswilson]

Bruce:

Going back to your post of 28 Oct at 2:51, where you wonder about simple averages versus RMS:

You are always correct, regardless of signal pattern, if you can sample torque and speed at high rates, multiply the products together, then take the simple average (mean) of these values over the time span of interest. (In certain situations, RMS calculations permit you to shortcut these lengthy computations.)

You say that you are sampling torque at 70 Hz, and that torque is cyclic at a few Hz. This seems to be to be a high enough sampling rate. You are effectively sampling velocity at 1 Hz. Now obviously the velocity varies far less than the torque, but your calculations essentially assume that the velocity is constant over this second. If it were constant, then (simple) averaging of the torque and multiplying by this velocity value is equivalent to multiplying each torque sample by the velocity and then averaging, and so would yield a correct average power value for the interval.

The question is: How good is this assumption of constant velocity over a second? Do you access to any better (higher frequency) measurements for the purposes of characterization? Also, it would be a good math exercise (I would just use Excel) to compare your averaging with exact calculations for various X% oscillations in velocity. You should make sure that the velocity curve lags the torque curve (a purely inertial load would lag 90 degrees).

Curt Wilson
Delta Tau Data Systems

 

[BruceDiesel]

Curt,

Unfortunately I don't have access to the data samples. The sampling is performed using electronics embedded in the device and the results are transmitted.

I agree, the sampling rate is more than adequate, even with the harmonics that would be present, the torque wave fundamental frequency is generally 1 - 2 Hz.

Thinking about what you are saying though makes sense - the torque curve does not change between the two environments as this is a function of the pedaling dynamics of a particular rider, but the velocity curve may change significantly due to the change in intertial loading.

I know on an indoor trainer - the coast down when pedaling stops is a lot quicker than on the road.

I guess one way to test this would be to place an LED and a sensor on the wheel (through the spokes) and take a look at the pattern on a scope.

 

[DaveScott]

BruceDiesel, I have toyed around on a spreadsheet (for fun!?), and basically I cannot see that the inertial load directly causes the discrepancy. However, I used a sinusoidal torque input and sinusoidal speed variation. What I did find is that for a small inertial load, the speed variation is larger and more in line with the torque variations, and for a large inertial load the speed variation is less, and lags the torque variation (rather obvious). Even if the phase angle in two cases was compared between 5 degrees and 85 degrees, there was little difference in power.

Thinking about where the discrepancy between inside/outside could lie, I can only imagine that the frictional force is not constant with speed, and 'outside' the speed variation is skewed by the power of three wind resistance, and is not sinusoidal any longer (effectively, the top of the speed curve is flattened), whereas if the inertia is larger, the speed does not vary much.
Another thought is that the torque input is not sinusoidal, either.

The flattened speed curve would give the same average. From my spreadsheet this shows a reduction in power for the high inertia load.

This could seem to conflict with your statement "coast down takes longer outside", which could mean that inertia is higher for outside. But I cling to the hope that coast down takes longer outside because the wind resistance is much less at lower speeds, and perhaps your indoor trainer has higher resistance at lower speeds?

I hope I haven't totally confused you, but it is quite an interesting problem.

 

[DaveScott]

//The flattened speed curve would give the same average. From my spreadsheet this shows a reduction in power for the high inertia load.//

That's confusing: it should say

The flattened speed curve would give the same average speed. From my spreadsheet this shows an increase in power required for the low inertia load, with same average speed.

 

[BruceDiesel]

For a lot of indoor trainers, the resistance increases linearly with speed (the resistance is based on magnetic/motor principle). There are new trainers that try to mimic the outdoor situation by using a turbine immersed in fluid - to create an exponential spead vs. resistance curve. The problem is that these trainers present significantly higher resistance than wind resistance so a coast down test would not provide any useful information.

You are saying though that there is an increase in power required for low inertial load - this is modelling our problem if I undertand you correctly?

 

[itsmoked]

Why does no one use a small generator (alternator) and just control the field or load to perfectly profile what is experienced on the road?

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[DaveScott]

//You are saying though that there is an increase in power required for low inertial load - this is modelling our problem if I undertand you correctly?//

I hope so. The effect, I think, comes from the higher speed 'pulses' which require ^3 more power. So to keep the same average speed, more power is required. If the trainer has more inertia, then speed will vary less. If the trainer doesn't have the same friction variation with speed, then it's probably even more different.

I checked the influence of phase shift torque/speed - v. little effect.
I checked the influence of calculation of speed more often - v. little effect. By the way, the speed sample every rotation seems to be OK. The torque samples must be made more often, since a once-per-rotation sample would not represent the rest of the rotation whereas the speed sample does represent the average of the rest of the rotation.

Magnetic braking: this may be more of a constant retarding torque, rather than a varying torque with speed i.e completely different compared to real world conditions.

 

[BruceDiesel]

This ties in well with anecdotal evidence that riders report - trainers with bigger flywheels present a more "road-like" feel.

These speed pulses could well be fatiguing the muscles more, the question is, how do we measure this? Given the limitations of the equipment that we are using.

In my mind a practical way to solve this is to develop weights that can be attached to the rear wheel of the bike. This would allow a rider to adjust the weights based on his body weight.

 

[itsmoked]

Measure the actual torque of a street rider then just map that to a generator control loop. Short and long term trends and all.

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[Skogsgurra]

Yes! That's how car companies run their test stands. Now, it's getting interesting!

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[TomG33]

I have been following this discussion with interest over the last day or so and spending some time pondering over just what is the real issue here.

From Bruce's initial statement and in his follow up posts it seems that the athelete can produce more power on the road as opposed to what he can achieve on an indoor trainer.
I am assuming that the levels of power are measured on the same bike using the same set of instruments in both cases.

Let me generalize for a while before getting back to specifics.
first up, power is defined as the the rate of doing work, and Work is defined as a force operating over a distance. (I know we all know this, but i like to define terms)
Now the way I see things is that the total work done is no different if the job is done fast or slow. At the end of the alocated time, the net work done is the same.
Lets think of two guys loading a pallet of bricks each, up onto a truck from the ground by hand.
Assume an impatient guy did it all in 20 minutes and then rested for 40, and compare him to a Plodder who paced himself and took exactly 60 minutes to do the job.
Now we look at the rate of doing work (or power). Over a 60 minute period, exactly the same amount of work was done in both instances, so by definition the average power is the same. (i am deliberately ignoring parasitic losses to keep it kind of simple ))
If you look at the instaneous power, though, you get a different story, Obviously the power profile will be nice and even for the guy that paced himself, where as for the impatient Fellow, he had a huge peak followed by a lull for 40 minutes.
Now in reality any two people doing such a task would each work at their own pace sometimes fast and sometimes slow and at different points in the cycle, but if they both did the same work in the same time frame they have both maintained the same FTP as Bruce Calls it.
Now I would assume that for elite athletes, Used to regular training, the variations in effort throughout the training session weather it be indoors on the trainer or outdoors would be minimal so I am fairly confident in saying that the minor variations mentioned by various people here will not really impact the total FTP in either situation. If the measuring equipment is doing it's job correctly then they should both read the correct power level for the duration.

I am a Motor & drives Kind of guy (28 years of it) and I have frequently come across statements along the lines that "one motor is delivering more power then another". The usual result is that the loads are different. Now one trueism about motors is
"A motor can only deliver power, that a load requires from it" The motor cannot "Push" excess power into a load if there is no need for it.

Now I see the athelete as being my Motor. He needs to output so much power to move his cycle along a road at given speed. If he goes faster, He will need more power, or if he starts to go up hill, he will need more power to maintain the constant speed.

So if he has a task to do in a set time (moving himself at a constant speed) he outputs whatever power required of the task. If it is easier (going down wind) then the power required will be less, because the losses will be less. If is fighting a head wind then the power to go a set speed will be higher.

I do not think Bruce says anything about different speeds, just different power output, so it could well be different environmental conditions requiring different levels of torque to maintain a given speed.

I keep mentioning constant speed because from my cycling days, i know that I felf more comfortable at a partivular speed, not faster, not slower, and i found myself tiring faster if i tried a different speed.
If you run a motor in constant torque mode, and the load drops, the motor will speed up until the torque of the load matches the motor torque, I do not think humans work this way.

Ok, So looking at the two different situations, What is different that could result in different torque requirements?

1
I am guessing that the outdoor track is level as would be the trainer, otherwise we wouldn't be having this discussion.

2
Obviously the outside ride will be influenced by the prevailing wind. whereas inside, the air resistance would be negligable.

3
What is the configuration of the trainer?. Do both of the cycle wheels turn or just the rear wheel? Does the rear wheel sit between two rollers or does it sit on top of a single roller?. What is the diameter of the roller?
I mention this because of what I call "Rolling Resistance". This is the extra forward force required to deform the cycle tyre as it flattens out due to the weight of the rider & bike on the road. A flat road will deform the tyre in one way, a small diameter roller will deform it in another way, and a large diameter roller even different again. Two contact points on the rear wheel will again be differnt as they are not on the bottom, but either side of the bottom. All of these things change the effort requred to move the cycle bearing a specific weight.

If the front wheel is not turning then it will offer no resistance to the forward motion meaning less torque is required to move at a given speed.

So my conclusion is that I do not think that your power differences are coming from the power measurement method but rather from the physical differences between the two activities. Two find the answer, You will need to define just how different the two situations are.

It is a bit long winded but I had nothing else to think about while sitting idle in a plane for a couple of hours this morning.

Tom

 

[TomG33]

This looked really goood for a while, until I realized that the adjustable load of the trainer will take care of all these differences, So it is back to the power measurement variation )
Tom

 

[BruceDiesel]

Tom,

For your background, the trainers we are using have two types of speed vs. resistance curves - trainers based on magnetic braking have a linear curve i.e. resistance is proportional to speed, and fluid trainer which have an exponential resistance vs. speed curve.

We are measuring power either at the cranks or the rear hub of the bike. The source of the resistance downstream of the measuring point should theoretically be irrelevant.

Speed is not really a factor due to the gearing of the bike, so all the athlete has to do is generate the watts for a period of time (the watts he can generate for 60 minutes being his functional threshold power (ftp)). At the end of the day the athlete changes gears in order to achieve the cadence they desire at the speed that produces the appropriate resistance (based on the speed vs. resistance curve of the trainer).

Interesting problem this one - I'd be interested to know why car companies test power the way they do?