I’ve Lost My Engineering Skillz!

I’ve apparently completely forgotten how to be an Engineer. In my last post about climbing Haleakela I screwed up the Drag calculation.

The advisor for the Purdue cycling club is a Professor in Physics and happened to stumble accross my blog about calculating power and pointed out the error I made.
I stated earlier that Drag has a square relation to velocity. This is still true, what I forgot to factor is that Drag is a measure of Force and not Power. This is easily solved as one of the methods of calculating power is by multiplying Force and Velocity.
This means that the Drag component of my power requirements do not have a square relation to velocity, but a cubed relationship.
Power(from Drag) ~ velocity^3
Earlier I stated that my Drag would have been 64% of Ryder’s, but with this new relationship it would actually be 50.9%. This further means that my portion of Power to counteract drag would have only been 12.3% of my overall output.
New average Wattage:
224.6 Watts
Thanks Prof. Hirsch

Maui Pt. 2

The volcano of Haleakala, at 10,000 ft and 36 miles it’s one long ass climb. I’ll just keep it short. In a nut shell: there was a lot of mind numbingly long climbing.

You almost have to start the climb early in the morning. The Trade Winds (whatever those are) are blowing a ton of warm air over the island this time of year, which means in the morning all the mountains start pretty clear, but by mid day they act as a conducting rod for clouds and rainfall. So unless you want to be swimming down the descent you have to start early. My parents dropped me off in the morning and were going to pick me up midway down to head back to the hotel. They also meet me at the top to see the Volcanic crater.
Once I got above 9000 ft people driving by would start slowing down and yelling out their car windows. One Asian tour bus pulled a long side and was taking a bunch of pictures.
So here are a bunch of pictures, and then I’ll geek out.
Long way to go from here

This is just about the hardest part of the climb, there are a gazillion switchbacks (Actually 23) before you even enter the park. And while most of the 36 miles is a manageable 5% or so, this few miles is like 7%.

Alright time go geek out.
A lot of people have power meters on their bicycles to measure how much power their putting through the pedals in order to measure their training. In leu of that I’m going to be doing some dimensional analysis to derive out my average wattage for the climb. Here is the Garmin info (unfortunately I forgot to turn on the stupid thing until I stopped for the first time)
More specifically here’s the info from the climb specifically (All in all I think it took me about 3 hours and 15 minutes with stops):

So first I’ll calculate the amount of watt’s I was putting out assuming a 3:15:00 climb of 10,000.
Given values are:
Weight: 150 lbs + 20 lbs (bike+water) = 77.1 kg
Height: 10,000 ft = 3048 m
Power is simply the amount of Work done/time
Work in this case will be calculated amount of Potential Energy change over the ride in Joules.
(Delta) U = mass * g * (delta) h
2305 (kJ) = 77.1(kg) * 9.81(m/s^2) * 3048 (m)
Then Power (neglecting any wind or bike+road resistance, and slowing down) is:
Power = (Delta)U / time (s)
197.0 (W) = 2,305,400 (J) / 11,700 (s)
Now it’s time to really stretch out some assumptions.
By comparison when Ryder Hesjedal did his Haleakela ride he finished in 2:32:51.
His power meter recorded an average 349 Watts. He is slightly heaver (160 lbs) but was using a nice Felt which probably weight 16 lbs, for a total weight of 176 lbs (79.8 kg).
Using the same dimensional analysis I used on my ascent his power output that went directly to climbing would be:
260 Watts
Meaning on average only 74.5% of his total energy output went to climbing the mountain, the rest was sucked up by wind and road resistance.
To calibrate my wattage I’ll neglect rolling resistance, since it’s usually pretty tiny, and focus on wind resistance. Drag has a squared relationship to velocity, D~v^2.
Ryder’s average ascent speed was 13.9 mph, while mine was about 11.1 mph.
This means that based on the square relation of air velocity alone my drag should be about 64% of Ryder’s, meaning that I used more like 16.3 % of my total energy to fight the wind and 84.7% to climb.
That would bump me up to 235.4 Watts for the climb
But that is not all, I am a lot smaller than him 5’10” to 6’2″. Which means he had a bigger sail. Form drag, or the amount of drag generated by an objects shape or size is a direct relationship to Drag. So assuming height is a good indicator of sail like ness, I have probably 94.6% the drag coefficient he does, further lowering my portion of Drag to 15.4% of my total power output
Bringing me back down a tick.
Final Estimated Wattage (using a hole mess of assumptions, which is how most Rockets are really built):
232.86 Watts
Not bad for a vacation ride