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

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 = 0.0115x**

^{3}- 0.0137x^{2}+ 8.9788xWhere "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.

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

ReplyDeletep = [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

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

ReplyDeleteIt 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.

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

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.

ReplyDeleteYes, 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.

ReplyDeleteCame 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.

ReplyDeleteI 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.

Why do you use a cube rather than a simple square to model this power curve? Say:

ReplyDeletey = 0.4 x^2 + 6x

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

ReplyDeletecarbon wheels

any one known the formula for MAG/MAG+

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

DeleteI 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.

ReplyDeleteWhat 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.

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

Deletedoes 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.

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

DeleteThis comment has been removed by a blog administrator.

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

ReplyDeleteI 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/

Delete