How are watts calculated?
 

Specifically, how are they calculated on cyclocomputer such as the HAC4?

watt = power = force * time... so its a function of cadence (time/rate of work), gearing, speed, and crank arm length (for force)...

atleast that's what i think

I always wondered that myself, how is the HAC going to distinguish slow pace while climbing up a big hill or beating into a 30mph headwind as opposed to just going slow.

But then again that may be why a HAC4 starts at $150 and Power Meter runs over $800....

Andrew

Well, I have the HAC4 (starts around $300 plus another $50 for cadence kit). I was a little suspect of the watts function, mainly because I had no idea how it calculates the watts. But then upon close examination of various pictures of the USPS bikes this year, I noticed that they use the HAC4. Based on that, I imagine it's trustworthy. Now I just wonder how ...

FYI - When configuring the HAC4, you have to enter your total weight (you + bike), but it doesn't know crank length or gearing.

Well, this is from www.hac4.com ...

HAC4 Power Output - The HAC4 calculates power output (in watts) by using the values of the combined weight of the bike, rider, clothing and accessories (as set by the owner), the gradient and speed. There is also a factor for the increase in air resistance as speed increases. The HAC4 of course does not know if you are riding into or with the wind but apart from this, the calculation of power output is accurate.

actually power is a change in energy over time. So it would be the integral of (force*dx) all over time. If you use Newtons, Meters and seconds, you should yield watts as a unit (lovely metric system). But yes, it is a function of those qualities. This nerdyness is what you get when you go to engineering school.

Watts are a unit of measure of work done per sec, which is the same as power.

the time is easily measured throught the use of a clock. The power is measured through comparing heartrate against speed (wheel and cadence) and calories.

If heartrate is not present then the power is an estimate based on an algorithm comparing, speed, calories consumed (from your weight - estimated), distance travelled and time.

any device not using heartrate and actual weight moved (should include the bike) is not an accurate measure of power.
Only SRM, Polar power kit and similar devices, closely measure actual power output.
The rest are vague estimates which serve no purpose.

You're right, I was thinking of the 434 and 434M, which also measures power but doesn't have the HRM functions.

I haven't used one, mostly because I'm concerned about it's accuracy in a place like Florida where there are no hills (but hearing that you can adjust for wind may make it a bit more accurate).

Is a great link that talks about measuring/training with wattage
http://www.midweekclub.com/powerFAQ.htm#Q5

And another site reviewing the Polar, SRM and PowerTap;
http://www.bike.com/template.asp?dat...ectionnumber=6

Andrew

This is exactly how the HAC4 the 434 and the 434m all calculate watts. I use the 434 and love it I allmost exclusively ride with the watts function on. I've found this to be the best judge of how I'm feeling, more so than HR. I have the cadence function also and use it to check if my watts go down or up depending on my gearing.

My CycliStats ride diary and training log (http://www.CycliStats.com ) estimates Average Watts for each ride, using a formula similar to that of the HAC4. You can download a free trial version from the website to see if it meets your needs.

Um..it's fairly straightforward to get a lower bound of power from weight and altitude gained, though the bound might not be tight. This result would certainly have a "purpose".

On the other hand, I can't for the life of me imagine how you'd get power from heart rate vs cadence w/o some serious per-rider calibration.

Care to enlighten us?

I don't think they use it for accurate power measurement... more for speed, distance, etc. I imagine. I suspect you'll see them using SRM systems in the off-season.

Thanks for this info as I've wondered how the HAC4 computes power. The HAC4 may get you into the ballpark, but it is not going to be as accurate as a powertap or SRM unit (you get what you pay for).

If you take a look at the online power calculator and power equation description at analyticcycling.com (there is also a site in Germany that has an excellent online calculator and description, and the details are in the book Bicycling Science, 3rd Edition, MIT Press 2004), you'll see that there are three components: One from rolling resistance, one from gradient, and one from aerodynamic drag. Rolling resistance is relatively small and you can make a reasonable guess based on tire type, total weight, and a nominal road surface. The contribution from gradient is a simple function of total weight and slope (both known based on the description of how the HAC4 is configured).

Power to overcome aerodynamic drag is going to be a guess, as the HAC4 cannot measure your projected surface area (how big an area you and the bike present to the wind), or the combined drag coefficient of you and the bike, or the veolcity of any wind. I will guess they use an estimate based on rider height, weight, and a "nominal" (whatever that is) value for the drag coefficient. If the HAC4 has an altimeter, it can make a reasonable guess for air density. Does the HAC-4 manual explain how this component of power is calculated?

BTW, heart rate doesn't enter into power calculations. If the rider is cranking 200w, that's what they're doing. Knowing your typical heart rate at various power outputs is useful, I believe, for training.

You can play with the online calculators or build a spreadsheet and see how big an effect changes in the assumed information can have on power. Now if someone had the time and money, they could do a side-by-side comparison of the HAC-4 along the lines of Bicycling Magazine's recent comparison of the SRM, Powertap, and Polar 720+power systems. (No surprise - they liked the SRM and Powertap.)

In the HAC4's database are the settings you provided on your height, weight, max heart rate, vo2 max etc.
Not sure of the formula but the powermeter compares your exertion (functions of your heart rate and cadence and forward speed) against an ideal curve. So for a rider of given mass, height, v02max etc at at given heartrate and cadence and speed he should be producing a given power output.

At least thats how i understand it.

Of course headwinds and gradient can't really feature because without pitot tubes and inclinometers feeding this info and adjusting for the changes in these, the info is irrelevant.

So even the best power meters amerely provide a best estimate and not an accurate figure.
The nice thing is however since the parameters measured are always the same, the power meter can accurately measure the change in your poweroutput an that is far more useful than the Actual Output.

AmpsXvolts=Watts

Actually, the best power meters (PowerTap & SRM) do measure accurate power input, by putting a load cell into the cranks (SRM) or the hub (PowerTap), so it's a mechanical measure of torque + rotational speed - all you need to precisely calculate power output (assuming the measures themselves are precise, of course). You can make approximations (such as HAC4), typically based on weight, speed and altitude change, and make assumptions for drag coeff, frontal area, rolling resistance, etc. Or you can use derived measures (I can't remember which comp uses this), by measuring chain vibration + cadence, to approximate chain tension, and thus calculate power based on chain tension and chain speed.

Now that's a really useful response.

Most of us produce mechanical power on a bike, rather than electrical power...

Tim is absolutely right. Electronics do not ever give you something for nothing, and without some kind of sensor for relative wind speed and gradient both of these factors will have to be assumed by the software in the microcontroller running the system. Wind speed would have to be taken from the speed shown and could not take into account any head/tail wind. I have seen some higher end computers which show gradient and altitude changes so that much could be included much easier. The best it can do is to assume a value for some of the variables and make a calculation. In the end, it is a ballpark guess which will give you a fair indication of what has happened.

Andy

I assume you're referencing the HAC4 and not the PowerTap or SRM units.

HAC4 watts = virtual or in 99% of real riding situations virtually worthless, not accurate and not repeatable.

PT & SRM Pro - each use 4 strain gages to measure wattage and torque giving you not only repeatable but accurate wattage assessment.