chinarider

On a ride that started & ended at the same place the other day, somehow I got into a discussion about the effect of hills on average MPH. The guy I was riding with maintained that on the course we were doing there was no effect as for every foot uphill there was a corresponding foot downhill, thus cancelling out the effect of the uphill. I regard him as a pretty intelligent guy, but I had a devil of a time getting him to see his error; I don't know if he ever really did. Which leads to today's assignment:

Assume a 2 mile course, 1 mile up & 1 mile down. Further assume you average 10 mph on the uphill portion and 30 mph on the downhill. What is your average speed for the 2 miles? Show all work. First right answer gets a gold star.

rumrunn6

I'm no good at word problems - can you draw a diagram?

steveymcdubs

Too lazy to show work. 15mph.

1nsane

first mile takes 6 minutes, second mile takes 2 minutes, 8 minutes traveltime covered 2 miles, 60/8 * 2 = 15 mph average

gazelle5333

At 10 mph uphill it would take you exactly 6 minutes to get to the top.
At 30 mph downhill it wold take you 2 min to get back to the bottom.
Thus 3/4 of your time is going up and 1/4 coming down.
And therefore .75*10 + .25*30 = 7.5 + 7.5 = 15mph average (I THINK)

lpolliard

First of all you are assuming and you know what effect that has. It makes an ass out of you and me (ass u me). But I have been called an ass on occasion so what the heck.

You are correct in disagreeing with your friend but the assignment will not prove your position.

Back to your question because I like algebra:
It takes 6 minutes to climb 1 mile and 2 minutes to descend 1 mile so total trip time for 2 miles is 8 minutes. This can be reduced to 4 minutes per mile which equates to 15 miles per hour.

rumrunn6

is that coasting down hill or pedaling?

Shuke

I was beat to it because it logged me out!

Would the average speed be 15?

Work:
10miles/60minutes=1mile/xminutes, solve for x, x= 6 minutes
30miles/60minutes=1mile/xminutes, solve for x, x= 2 minutes

Total elapsed time: 8 minutes
Total distance traveled: 2 miles

2miles/8minutes=xmiles/60minutes, solve for x, x= 15

Average speed= 15 miles/hour.

One (your friend) would probably think that the average speed would be 20mph but it takes a disproportionately smaller amount of time to descend than to climb meaning you are holding a much higher velocity but it is affecting your average less.

chinarider

1nsane

Yeah I Win! Ill take the dishwasher.

chinarider

yep. Same principle applies to head & tail winds.

grwoolf

You friend is wrong. I'll ignore the assignment because it doesn't really prove or disprove your friend's statement and would require math. However, the one flaw I can see in his logic is that he isn't accounting for the resistance of the air.

Going uphill, you obviously suffer from the effects of gravity. Going downhill, you get the gravity assist, but that is quickly reduced as your speed goes up and air resistance builds exponentially.

chinarider

[QUOTE=1nsane;10902496]Yeah I Win! Ill take the dishwasher.

I only promised the star.

rumrunn6

regardless, I sweat less if I'm on the bottom

chinarider

Hey, I resemble that remark. Its my assignment and I'll ass ume whatever I want!

colombo357

This is where you went wrong.

chinarider

I guess. When I was trying to explain it, I thought it was pretty obvious & this thread proves it was. Maybe it was oxygen debt.

black_box 

Except you've arbitrarily chosen your speeds. Wouldnt it make more sense to maintain constant power output? and as already stated, faster speed = more energy lost to wind resistance. The potential energy you stored going up the hill is not converted back to kinetic energy at 100% efficiency.

lpolliard

Riddle me this Batman???

If Newton's Law states that two objects of differing mass will fall at the same speed (in a vacuum) then why does a heavier cyclist descend faster than a lighter cyclist?

My guess it has to do with wind resistance.

ptle

How long has he ridden? Tell to climb a mountain then come back down. Then do the same amount of distance on a flatter course.

chinarider

Probably. I picked the numbers to make the math easier. I realize there are a lot more variables. But the same principle still applies. You will spend more time going up than down, thus your average will be closer to the uphill speed.

apricissimus 

But the more important fact is that while you are going slow uphill, you are doing so for a longer period of time. And when you are going fast downhill, you are doing so for a shorter period of time.

Quel

Climb I did last weekend was ~8mph on the way up and ~40mph on the way down. That part at 40mph is not nearly long enough to make up for all that climbing.

chinarider

You answer your own question, Grasshopper. They're not in a vacuum.

chinarider

Yep, its not the fact that you are going uphill or down, its the time spent doing so. Another example that takes the wind resistance, etc variables out of the equation. Drive your car 30 miles @ 30mph on a perfectly flat road. Turn around and drive back @ 60 mph. Your average speed isn't 45.