If you had two 12 mile loops
Loop 1. Is completely flat except for a 200’ hill at 12% grade.
Loop 2. Is completely flat except for a 200’ hill at 5% grade.
Which would most ride at a faster average speed?
Why do people insist on asking stupid questions?
how fast can you ride will determine which ride is faster. think about it. 12% 300’ and 5% 300’ means that for every 100’ feet you travel you will either go up 12 feet or 5feet of elevation. You tell us which one is faster.
It certainly depends on the ability level of the rider, but I would think that loop 1 would be faster for a very strong rider. If someone is a weak enough rider, then his/her speed will approach or reach zero on the 12 % grade, and that would certainly result in a slower result.
To clarify.
- Don’t really think it is a stupid question
- These are uphills. The down hill would be identical for both.
- Interested in the average speed for the entire loop not just how fast to climb the hill.
Basically if you have 200 feet to climb over 12 miles which results in a faster average speed. A quick climb of the 200 feet or a slow climb.
This is a great question!
According to my calculations, the 5% grade loop is faster by about 20 - 40 seconds.
- The 200’ elevation change is actually climbed in shorter time on the 12% grade (by about 30 seconds)
- But the 12% grade loop has 0.44 miles more of flat riding (assuming the same downhill) which takes about a minute longer.
I used www.analyticcycling.com and ran 200, 300, 400, and 500W with 75kg and the 5% grade loop is faster for all (~40 seconds for 200W and ~20 seconds for 500W).
Edited: OK I totally botched this the first time, here’s a corrected version, and the difference is bigger than I suspected.
The assumptions are the defaults from analyticcycling:
bike+rider=75kg
power output a constant 250 watts
asphalt road, average frontal area & drag, sea level etc.
and…instantaneous transitions in speed when transitioning between climbing, descending and riding on the flat
The details:
Your 200 foot hill is ~61 meters high
on the 5% grade the hill spans ~1220 meters (up, then 1220 down) meters, for the 12% grade, about 508 meters up then 508 down.
speed up the 5% grade is 5.61m/s
speed up the 12% grade is 2.71m/s
time up 5% 217 seconds
time up 12% 187 seconds (steeper, you go slower, but the climb is shorter in length)
speed down 5% 17.69m/s
speed down 12% 24.94m/s
time down 5% 68 seconds
time down 12% 20 seconds
total time on 5% up/down 286 seconds
total time on 12% up/down 208 seconds
which sounds like a lot…but…
remaining distance on 5% course: 16.872K, @11.23m/s = 1261 seconds on the flat
remaining distance on 12% course: 18.295K, @11.23m/s = 1368 seconds on the flat
grand total 5%: 1788 sec (24.15 mph)
grand total 12%: 1837 sec (23.51 mph)
difference: 48 seconds in favor of the 5% grade
According to my calculations, the 5% grade loop is faster by about 20 - 40 seconds.
Something’s wonky because I came to the opposite conclusion, using the same tool (see above) - I think I found an error in my calculation though, I have the remaining flat distances wrong, since I only subtracted half of the climbing distance.
If you had two 12 mile loops
Loop 1. Is completely flat except for a 200’ hill at 12% grade.
Loop 2. Is completely flat except for a 200’ hill at 5% grade.
Which would most ride at a faster average speed?
hmmm … can it be a loop without the downhills?
if you’re simply asking which is faster to climb, a 200’ hill @12% or a 200’ hill @5%, then ceteris paribus - the 12% grade will be quicker.
Man and I thought my discrete math class was worthless, turns out it helped me understand something.
To atone for screwing up the original answer (and in a slightly dismissive way), I offer the calculation for a similar loop, but one in which the climb to 200 feet is 12% from one direction and 5% from the other, pondering which direction would be faster to ride in…
And (I think) the answer is, for the 75kg bike+rider and 250 watts, it’s faster to ride up the shallow long hill and down the short steep hill, by 19 seconds. Which I find slightly counterintuitive. For a Contador-ish 65kg/400W the gradual up and steep down is faster by 10 seconds.
As to why it seems slightly backwards - if someone challenged you to a head to head race where you could either pick running up 100 feet of stairs and then down a nice 2% slope for 1500 meters OR up the 2% slope for 1500 meters and then down the stairs, which would you pick? I think I’d pick up the stairs and then down the gentle grade…which might be wrong…or it might be right and the difference in the bike problem is air resistance and the fact that it varies with the cube of velocity.
The shallow, longer hill results in a faster overall time (let’s forget loops and just say it’s a 12mile course that is flat until the 200’ hill and finishes at the top…also assume constant wattage by the rider, no change in position ).
The reason for this is that the longer hill results in more time at a lower speed where wind resistance is exponentially less (both courses have the same vertical work).
The fastest course would be a 12 mile constant grade that climbed 200’.
Thanks for the calculations. I was guessing the 5% grade would be faster and looks like it is. But had little to backup my guess.
I was not really interested in the downhill portion. The reason for this is I was guessing what avg speed I would exceed for a race this week-end. I have a race this week-end with about 600 feet of climbing but at a very low grade. I train in a park with great hills and have the same feet in climbing but the grade is much greater. Probably something like 5% for the race course versus 12% for training course.
I average a little over 21mph on my training course and wanted to set my timing goals based on exceeding this but wanted to be sure it was practical.
If you had two 12 mile loops
Loop 1. Is completely flat except for a 200’ hill at 12% grade.
Loop 2. Is completely flat except for a 200’ hill at 5% grade.
Which would most ride at a faster average speed?
I don’t understand the question. The hill is the same length but one is steeper? Wouldn’t you go faster on the less steep hill?
200 feet is the altitude gained, not the length, so the 12% grade would be shorter but steeper.