Thursday, December 17, 2009

No power meter? Just use your home trainer!

While we wait for better and cheaper power meters to come on the market, what options do we have?  Ed has kindly demonstrated that the Sporttracks Power Analysis plug-in may actually be pretty accurate. Plus or minus 3%, wow!

Another way of quantifying power output and "getting a feel" for the numbers is to use a fluid trainer


The resistance in a fluid trainer is a function simply of speed; the faster you go, the more the resistance you get.  Magnetic trainers on the other hand use a variable resistance to provide adjustable resistance.  An advantage of this is that resistance can be programmed, so that you can simulate the ups and downs of your favourite ride, with video cues as well, turning it into a virtual reality trainer, such as those made by Tacx and Computrainer

The main disadvantage with magnetic trainers is that they don't really feel like riding on the road, which is why I like my CycleOps Fluid2 fluid trainer.  Turning the drum on this trainer with your rear wheel forces an impeller to turn in a sealed drum full of silicone liquid.  This, coupled with a flywheel, somehow manages to give somewhat of an acceleration and inertial feel of the open road. 


It turns out that fluid trainers have a fixed relationship between power and speed. Some manufacturers actually publish a curve, like this one for the Fluid2:






One company, Kurt Kinetic, actually makes a "Power Computer" which, if it actually measured power, would be by far the cheapest on the market, at USD $79.99.  Unfortunately, all it does is convert the speed signal to a power number based on the characteristic curve for their trainer unit.   Kurt Kinetic has even gone trough the trouble of determining characteristic curve equations for competing trainers, so you can use their computer with those.  Unfortunately, the equation they provide for the Fluid2 looks nothing like the curve above, leading me to believe that they must have used a much older unit.

Unfortunately, the nice folks at Saris, the maker of the Fluid2, haven't published a table or an equation that would allow me to easily determine my power given my speed on the trainer.  Perhaps this is because they would rather you buy their $2000 Powertap powermeter? Anyhow, I picked a few numbers off the graph above and put the numbers in an Excel Spreadsheet to find that the curve is very nicely modeled by a third-order polynomial equation.  This one:

y = 0.0115x3 - 0.0137x2 + 8.9788x

Where "y" is Power, and "x" is speed in MPH.

Adding a column for speed in KPH yields the following:

x
y
Speed
Speed
Power
kph
mph
W
0
                0  
0
1
              0.6
6
2
              1.2
11
3
              1.9
17
4
              2.5
22
5
              3.1
28
6
              3.7
34
7
              4.3
40
8
              5.0
46
9
              5.6
52
10
              6.2
58
11
              6.8
64
12
              7.5
71
13
              8.1
78
14
              8.7
85
15
              9.3
92
16
              9.9
99
17
             10.6
107
18
             11.2
115
19
             11.8
123
20
             12.4
132
21
             13.0
140
22
             13.7
150
23
             14.3
159
24
             14.9
169
25
             15.5
179
26
             16.2
190
27
             16.8
201
28
             17.4
213
29
             18.0
225
30
             18.6
237
31
             19.3
250
32
             19.9
264
33
             20.5
278
34
             21.1
292
35
             21.7
307
36
             22.4
323
37
             23.0
339
38
             23.6
356
39
             24.2
373
40
             24.9
391
41
             25.5
410
42
             26.1
429
43
             26.7
449
44
             27.3
470
45
             28.0
492
46
             28.6
514
47
             29.2
537
48
             29.8
561
49
             30.4
585
50
             31.1
611

And now I can "train with power" on my home trainer, without a power meter, as long as I move my speed sensor to my rear wheel.

16 comments:

  1. That's very helpful! I've got a more detailed breakdown for Kph if you want a bit more granularity (matlab):

    p = [0.0115 -0.0137 8.9788 0]; % Polynomial
    kmph = 0:0.1:50; % Kilometers per hour
    mph = kmph / 1.609; % Convert to MPH

    y = polyval(p,mph); % Power output y

    plot(kmph,y);

    for k = 1:length(kmph)
    fprintf('%0.1f,\t %0.1f\n',kmph(k),y(k))
    end

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  2. Does the torque on the roller against your wheel affect the curve?

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  3. It shouldn't make a significant difference as long as the roller is not so tight that you are deforming the wheel or hub. If properly adjusted, the friction between the roller and wheel will be negligible compared with the energy required to run the trainer.

    Here's a good article on how to properly adjust the tension: http://jimlangley.blogspot.com/2009/03/q-indoor-trainers-cliff-house-tandem.html

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  4. Nice post. TFS. I have one, maybe stupid question. Is this related only to speed? What happens if I change gears on the bike while riding? Obviously to keep up the same speed in a difficult gear will mean more power output.

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  5. Yes, it is only speed related. If you change to a higher gear and keep the same cadence, the speed goes up, as does the power, in accordance with the curve above.

    ReplyDelete
  6. Came across your post when trying to follow my Power-training program, without a power meter! I had done the same thing as you, pulled a number of points of the Cyclops power curve, just to realize that it was complete bullshit, unless I had become excessively weak from my last power test.

    I used a SRAM crank powertap. The result for my Cyclops Fluid 2 trainer (from Aug. 2011) Power = 1.5981 x + 0.006942 x^3, where x is tire speed in km/hour. 100psi in the tires. This curve is rather steeper than the one from the Cyclops, but not quite as steep as the one from Kurt Kinetics.

    Whether people can use this curve for their own Fluid 2 is not certain, since Cyclops may change their oil sligtly, or even design between models.

    ReplyDelete
  7. Why do you use a cube rather than a simple square to model this power curve? Say:
    y = 0.4 x^2 + 6x

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  8. There is lot of articles on the web about this. But I like yours more, although i found one that’s more descriptive.
    carbon wheels

    ReplyDelete
  9. any one known the formula for MAG/MAG+

    ReplyDelete
    Replies
    1. You can probably figure it out from here: https://www.cycleops.com/post/blog-15-cycleops-science-resistance-curves

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  10. I just came across this article. The last couple of weeks I worked on a fluid2 with my son's power meter data. I basically find the same formula as described above although a X2 equations has the same accuracy.
    What I found counter intuitive is to see lower power level for a given speed when the trainer is cold (thicker oil). You need to run the trainer a good 15mn before having stable data.
    The real challenge with the accuracy is when you reach speeds of about 30km/h. The curve is very steep and a small variation in speed has a big variation in power. 52x19 at 80rpm is 28km/h or about 165W. At 90rpm the speed is 31km/h or about 220W.
    Any small variation in the equation parameters has a big impact on the resulting power.

    ReplyDelete
    Replies
    1. As long as the resistance in the trainer is held constant, the power will vary directly with the speed. SO, for example at 5 mph the power will be exactly half of that at 10 mph.This assumes the resistance
      does not vary with time or speed.( eg no road wind considerations)IN THE ABOVE example therefore, 163/28= x/31
      or x=163x31/28 =182. Therefore in that case the resistance had to go up with increasing speed.It would be best to avoid
      trainers with this characteristic as it makes
      the power calculation dicey and likely less
      reproducible. With constant resistance trainers you can use speed as a reliable
      measure of RELATIVE power due to the considerations above.

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    2. Actually not quite right for a fluid trainer. In a fluid trainer the power varies with wheel speed in accordance to a curve determined by the design of the trainer. CycleOps has a great article on the different characteristics of different types of trainers. https://www.cycleops.com/post/blog-15-cycleops-science-resistance-curves

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  11. This comment has been removed by a blog administrator.

    ReplyDelete
  12. Does anyone know if there is a place one could obtain up to date power curves for a wide variety of trainers?

    ReplyDelete
    Replies
    1. I haven't seen any. The best option would be to make a curve using a borrowed powermeter. Obviously the good folks at Zwift and Trainer Road have gone through the trouble. And have a look at this: http://www.powercurvesensor.com/bikestudio/

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