# Watts per Kilogram

We all know that the most important metric for any competitive cyclist is watts per kilogram (w/kg).  How many watts a cyclist can produce per kilogram (or pound) of body weight is a big determinant of how fast the cyclist can go.

This is especially true when climbing.  On flat terrain, body weight doesn’t factor in as much as raw power output.  Most road races here in the northeast are quite hilly, and the outcomes are usually determined by the climbs.   Since I outweigh most of the guys that beat me across the line, I’ve always been keen on seeing actual data that shows how much more power I need to generate to keep up with the more nimble riders that I compete against.

Physics says that if two cyclists were to climb the same hill, at the same w/kg, they’ll go up at the same speed.  So on a given climb, if one cyclist weighs 65 kg (143 lbs), and produces 300 watts, that would give him 4.62 power-to-weight ratio.  A second cyclist weighing 80 kg (176 lbs) would have to generate 80 * 4.62 = 369 watts to match the speed of the more nimble cyclist.

Ouch.

Let’s put physics to the test, shall we?

I have two data files from the recent Housatonic Hills Road Race – a very hilly affair.  One file is that of my fellow teammate Tom, who finished 6th.  Tom claims to weigh a scant 68 kg (150 lbs).  The other file is my own.  I weigh 78 kg (172 lbs), or 14.7% more than Tom.  So if I’m to keep the same pace as Tom up the hills of Housatonic, I need to generate 14.7% more power, right?

Let’s look at the first climb up Constitution Hill.  This is only the first part of the climb – the steeper part.  Here is Tom’s data:

Now, here’s my data for Constitution Hill:

Same distance (0.75 miles), and (roughly) the same time.  Tom’s average power was 292 watts, while mine was 318 watts.  318 / 292 = 1.09.  So I had to generate 9% more power (26 watts).   That’s less than 14.7%, but we haven’t taken into account the weight of the bikes, bottles, and whatever we were both carrying.

Let’s do another.  Here’s the steep portion of the climb on Minor Bridge Road.  First, Tom’s data:

Now, my wattage for Minor Bridge:

Again, almost identical time and distance.  Tom’s power was 381 watts, and mine was 409, a difference of 28 watts.  409 / 381 = 1.073.  So I required just 7.3% more wattage.   I didn’t expect this one.  I thought the steeper sections would require more power on my part.  Did I drink more of my water bottle than Tom?

Now let’s take a look at the KOM climb.  Here’s Tom’s data:

And now my KOM data:

This KOM comparison is a little different than the previous ones.  We climbed the same distance, but Tom scaled the KOM climb 7 seconds faster than I did.  My 24 watts (7%) above his wasn’t enough to keep pace with him.  To get a more accurate comparison, let’s look at Tom’s KOM climb on Lap 2:

Tom’s second lap KOM was 335 watts, and only about 1 second faster than my KOM on lap 1.  382 / 335 = 1.14.  Look at that.  The 14% difference in wattage matches our difference in weight.  So I needed 47 more watts than Tom on this climb to keep pace.  Interestingly enough, the KOM climb is a constant grade (for the most part).  More so than any other climb compared here.

Let’s do one more –  Constitution Hill on lap 2.  Here is Tom’s data:

And now mine:

Once again, same distance, and our times were roughly equivalent (Tom was 3 seconds faster).  Power ratio: 337 / 312 = 1.08.  The 8% increase in wattage (25 watts)  closely matches the first Constitution Hill comparison above.

Here’s a summary:

Climb Tom Justin Delta %
Constitution Hill, Lap 1 292 318 26 9.0%
Minor Bridge (steep section) 381 409 28 7.3%
KOM 335 382 47 14.0%
Constitution Hill, Lap 2 312 337 25 8.0%

Once again, I weigh 14.7% more than Tom.  This difference is in body weight only, and does not account for differences in bike weight, or anything we were carrying (bottles, etc).

It seems that I needed a minimum of a 7-9% increase in power to match Tom’s pace up most climbs.  It should be noted that the grade (steepness) on the Constitution Hill and Minor Bridge climbs varied.  Both climbs had sections that flattened out a bit.  The KOM is a much steadier climb, with a grade that barely changes.  It is interesting to note that on that climb, the additional power required more closely matched the difference in body weight.

So what does it all mean?  Well, if you’re a rider that gives up 20+ pounds to any other rider, be prepared to generate at least 25-50 watts to keep up.  That’s a lot.  Next time you do intervals, try increasing power by just 10 watts and see how difficult it is.

What if you’re a heavier rider and can’t generate enough additional power?  Well, look at both Tom’s and my KOM climb from lap 1.  I only generated 24 watts more than he did, and Tom beat me up the hill by 7 seconds.  This is why starting at the front of the field on climbs is so important.  If you drift back in the field (get passed by everyone), there’s a great chance you’re still in contact, even though you’re 7 seconds slower.  If you start at the back of the field and take 7 seconds longer, you’re either chasing, or you just got dropped.

Welcome to my world.

1. Okay, from the peanut gallery…..

How much would it take to get me up the hill with your featherweights?

I weigh 195 or 88.45 kg.

John

Could be why I struggle on the hills?

2. John – at 195, you would have to push 456 watts to match Tom’s 335 watts.

3. @SFB Unfortunately for you, Bill is right. For the 3-minute KOM climb, you would have to generate 456 watts to keep up with Tom if he went up at 335 watts.

335 w / 65 kg = 5.154 w/kg * 88.45 kg = 456 watts

I know you, and you’ve got that kind of power. The problem is not pushing that kind of wattage on one hill, but doing it on climb 6, 7, 8….

Now you know why all the guys leading the climbs on the pro tour have arms that look like toothpicks.

4. @ Justin – very well illustrated! Thanks very much for putting this together.

Running out of excuses for poor climbing performances? Check here for some fresh ideas

5. Justin:
Good stuff. Been off the bike for a few weeks becasue of my knee and gained weight. God and my parents did not bless me with the correct body type for bike racing but when I do slim down the climbing results are dramatic. 10lbs allows me to make huge gains in performace. Just have to take off those 10lbs. Our friend Muzz is a powerhouse @ 180lbs he still hangs with the 140-150lbs. guys while going up.

6. Our buddy Muz is both strong and efficient. But I can attest that he still has to work much harder than those lightweights. I’ve climbed next to him quite a bit in races and can almost always hear his heart beating (when it’s not drowned out by his breathing).

7. This calculation is good as a guideline for p2w ratio but would be made much more accurate if you took rolling resistance (which will vary with weight) and aerodynamic drag (the larger rider would generally have greater drag) in to account. Nice job thought! 😀