watts = (kg*9.8*e/t)+(kg*9.8*e/t)*r
This is the formula to help me find my goal for Paris Mountain success. It isn’t perfect, but it gives me a pretty good idea of how many watts I need to average while climbing the 2 miles and change to the top of Altamont Road. I’ve been playing around with it and have started landing some consistent results between what my power meter records and what the physics tell me should happen.
Math and cycling does mix!
Saturday, I weighed in at around 195. No, I don’t weigh that much. That is Me + Clothing + Water bottles + Saddle bag + Bicycle. All 195 pounds of me headed down the road toward Paris Mountain. The plan for the day called for a couple of repeats up Altamont Road. Granted, I was going to be exceeding the time of 12 minutes the plan called for, but I wanted to go all the way to the top.
watts = (89*9.8*e/t)+(89*9.8*e/t)*r
The first part of my equation was in place. 195 pounds is equivalent to about 89 kilograms (88.63636 to be exact). Of course, gravity doesn’t change. So, the second part of the equation was in place a long time before I was ever born… 9.8. Each time you climb the mountain you feel its effects. It is always working against you to keep you from getting that time you want.
watts = (89*9.8*241/t)+(89*9.8*241/t)*r
Another constant was waiting for me as I turned right onto the well traveled road. I knew that I would be climbing 790 feet — or 241 meters — over the next 2 miles. Oddly, the distance doesn’t really factor into the equation. The distance can also vary from as short as 1.9 to 2.2 depending on how you take the turns to the top. Typically, the distance I cover is around 2.1 miles. Regardless, I was going to be climbing 790 feet.
It was now time to introduce the largest variable into the mix… time. Time working within the equation would make all the difference in the result. It was up to me to make it happen.
Because I didn’t push on my way to the mountain, I was feeling pretty good. I started the climb in a little harder gear than normal. My goal was to climb at a pace that would keep the pedals turning over and try to maintain my momentum to keep from getting bogged down.
As I reached the top of the water tower section I noticed I was sitting at around 3:30. That was good… or maybe it was bad. It was good because I normally come across that section about 15 seconds slower. It could be bad because that might mean I was pushing a little too hard too early.
Still, I kept feeling strong as I reached the false flat just before the halfway point. Nice! I reached the halfway point at about 5:45. I knew now that even if I finished the second half in my normal time, I would beat my more recent attempts.
I kept trying to keep my momentum, but I did have to shift to easier gears at points. I also lost track of time. At the section where I normally start faltering — about two-thirds up — I felt pretty good about my time. Still, I didn’t know how to judge if I was slipping back or keeping the good time. The base of the wall would be my answer.
I reached it in under 12 minutes. Now it was time to give it all I had up the wall. It is amazing how much time you can lose laboring up the steep grade. You have to save a little something for this section or it will crush you.
watts = (89*9.8*241/763)+(89*9.8*241/763)*r
12 minutes and 43 seconds was the time showing on my Garmin. That translates to 763 seconds — the measurement I needed to complete the equation. By the way, it was my best time of the year so far.
So, why don’t I have the watts listed? Well, take a look at that little “r”. It stands for resistance. It isn’t just gravity working against you. There are various forms of resistance keeping you from fighting just against the pull of the earth. Wind is one factor. Road surface is another. I also throw in there the variations of my power meter. It could be as much as 5 percent off of the actual physics involved.
I have arrived at “r” by doing repeated climbs and comparing the power meter wattage with the formula. Typically, you should add 10% to the formula. However, I found that all other variables being known, 10% was a little too low. At least on Paris Mountain I found 15% to 18% to consistently return an equation wattage comparable to what my power meter gives me.
323 watts = (89*9.8*241/763)+(89*9.8*241/763)*.17
Here is where the math can drive you crazy! You can start playing around with the variables to get an idea as to what type of wattage you need to put out in order to get a certain time. I’ve always dreamed of making the climb in 11:15. Just insert the time 675 seconds into the equation and you get a return of 366 watts. Can I hold 366 watts for that long?
You can also start playing around with other variables. For instance, what happens if I drop 5 pounds? Ah, 356 watts gets me to the top within my goal. Interestingly enough, I was about 5 pounds lighter when I made my personal best of 11:24. At that time, I averaged 352 watts to the top.
Of course, all the math goes out the window when you start the climb. The road is not a simple steady incline. You can’t just get on a track and hold a certain consistent average. Sometimes you are laboring to get the pedals to turn over while producing 450 watts. At other times you are spinning away looking for more gearing and down around 250 watts.
The math doesn’t help unless you have proper technique and fitness. However, this what makes it fun! You can always work to improve both of those and then you get to see the results of your labor in that one little result: watts = (kg*9.8*e/t)+(kg*9.8*e/t)*r.