I am an avid bicyclist and ride about 30 miles per day. Something I’ve always been curious about is the significant drop in average speed when riding in hills versus riding on flat roads. Why does this happen?
I have two rides that I alternate between. Both are about 30 miles. When I ride South the terrain is flat as a pancake. When I ride North it’s pretty much all climbs and descents. Some of the climbs are brutal. On my southerly ride I can average 20 mph with very little effort. On the northerly ride I can go all out and not average more than 13 mph.
Since both rides start and stop at the same place (home), the elevation change from start to finish is the same (zero). It seems to me that the time lost in a climb would be made up for in a descent. Obviously this doesn’t happen, but why?
You probably don’t pedal on the downhill side, you probably are using your brakes. So you are not taking advantage of all the potential energy you built up with all the great effort going uphill.
And even if you’re freewheeling (or even pedaling) downhill, air resistance is much greater when you’re moving faster — so the air does much more work against you when you’re descending than when you’re ascending.
You do realize that the actual distance you travel on hilly terrain is greater than if you travel perfectly horizontal don’t you?I assume you measure your distance with GPS.
I should add that hilly terrain roads are generally not straight either.
I would assume otherwise. Bicycle computers measure wheel rotations, so would give a true rolling distance.
There is the old riddle about calculating average speeds. You’re on a two-mile stretch of road. You drive the first mile at 30 mph. How fast do you need to drive the second mile to average 60 mph over the two-mile distance?
What’s your average speed when riding downhill compared to your average speed riding up? There’s a hill I ride that I average about 10 mph up and a touch under 40 mph going down. That tallies with a total average of about 20 mph, but when I’m going down, to achieve that 40 mph average I need to pedal like I’m being chased by a swarm of angry wasps and my max speed needs to be up around 45-50 mph to compensate for the corners where I need to slow down. Basically, I have to ride HARD, really hard, to achieve a speed that comes close to compensating for my speed loss going up. I’d guess that you just aren’t riding that hard going down the hills.
Also, in case it’s not clear, if you are going at half your usual average when climbing, you need to double your average when descending.
Hah! It’s infinity. Infinity miles per hour. (To average 60 mph, the 2 mile course should take two minutes. However, at 30 mph it took two minutes to travel just the first mile, so there is no time left)
The above posts have it right. Essentially, its a consequence of the meaning of “average speed”, and how the math involved works out.
For example, if your average speed going level is 30 mph, your speed going uphill is 20 mph and your speed going downhill is 40 mph, then a course that was exactly half uphill and half downhill would be ridden with an average speed of about 26 mph.
It’s because you spend more time going slower that the math works out like this.
And that’s the one-line answer to the OP’s question.
Averaging different speeds can lead to some non-intuitive answers. If you ride 10 mph for a mile, and then 30 mph for a mile, you can’t just average 10 and 30 to get 20 mph. That’s because the unit “mph” also includes time. And it’s the time you spend going each speed that has to be averaged. So the first mile took 6 minutes, and the second took 2 minutes. The resulting average is 2 miles in 8 minutes, or 15 mph. Notice the average speed over that ride is far closer to the slower speed, because you spent triple the time going that slow.
For that reason, hills always reduce your average speed. Even cancelling all the elevation change by doing an out-and-back doesn’t buy back the time you have to put in climbing. You can’t spend enough time on the descents to really boost your average speed.
Ah, but you are forgetting that relativity is, well, relative. Time will dilate for the traveler at that speed, but time will proceed as normal for the guy standing on the side of the track with the stop watch.
I try to keep my speed when climbing above 10 mph. There are a few hills that are too steep for that, though. The most brutal climb is about 4.5 miles long, and I don’t think I’ve ever been doing more than about 5 or 6 mph when I approach the top of that beast.
You are right that I am not riding hard in the descents. Usually I’m coasting and enjoying the scenery. I usually top out around 40 mph on a particularly steep downhill run.
Thank you for this explanation. I’ve also noticed the same effect (although to a lesser degree) with a strong wind. I guess the explanation for that is about the same.
This counterintuitive effect is well-known among pilots.
It would seem that if you fly from A to B with a 20 knot headwind, and then return from B to A with a 20 knot tailwind, that you will make the same time as if there had been no wind at all.
However, in fact the combined effect of the headwind and tailwind is a longer travel time and more fuel used.
For example, if A and B are 100 miles apart, and you cruise at 100 knots TAS, each leg will take 60 minutes with no wind for a total of 120 minutes.
With a 20-knot wind, the times are 100/80 + 100/120 = 75 minutes + 50 minutes = 125 minutes (an extra 5 minutes and an extra 4% fuel over the no-wind case). Even though your “average” headwind has been zero!
(In fact your average headwind - correctly measured by time, not by distance - is not zero.)
If the hill was steep enough your avg speed would approach zero mph and that is the gist of why.
Energy goes into fighting gravity first and you have to put in enough energy to just stand still, then more to move forward, that energy to stand still does not help your progress. Think of a hovering rocket ship, using lots of fuel (energy) but not going up - it’s a amazing thing to see a rocket hover - such power to just hang there.
MikeS deserves extra credit for the only person to mention the cause of the effect in Frosty Camel’s OP. The averaging equations are all correct, but they don’t explain why the increased speed going downhill doesn’t compensate for the reduced speed going uphill. The answer is because drag due to wind resistance is proportional to the square of velocity - this is why professional cyclists don’t expend huge amounts of precious energy trying to take the downhill sections as fast as they can, as they know the law of diminishing returns kicks in.
If we have a downhill section followed by an uphill section, and both have the same top-to-bottom distance and slope, then the time taken to traverse this is exactly the same for the same distance over the flat, if we ignore friction and inertia. Let’s define the following:
V0: Velocity at the top of the downslope at the start.
V1: Velocity at the bottom of the hill.
V2: Velocity at the top of the upslope at the end.
s: Distance travelled on each slope.
a: Acceleration due to gravity (here a=g*sin(theta), where g is gravity and theta is the slope angle).
t1, t2: Times taken to traverse the downslope and upslope respectively.
Using two general equations of motion s=t(v+u)/2 and v=at+u (where u = initial velocity and v = final velocity) and plugging in the above variables we can arrive at:
(V1+V0)(V1-V0) = (V1+V2)(V1-V2)
In other words, the initial velocity V0 is the same as the end velocity V2. Similarly, the times taken to traverse both slopes are identical, so the average speeds on both slopes will be identical. Now back in the real world we have the accursed effects of air resistance to deal with. In the above example (and still simplifying things a bit, as I’m still ignoring the rotational inertia of the wheels and, to a much lesser extent, the bearing friction and rolling resistance of the tyres), air resistance will have the effect of lowering the velocity reached at the bottom of the slopes, so the time taken to traverse hilly terrain will be longer than the equivalent distance on the flat.
In summary, hills are a bummer. To make the most of a downhill section the best approach is to reduce the effects of wind resistance by minimising one’s frontal area: head down, elbows in. Frosty Camel is wasting no effort by coasting downhill and enjoying the scenery.
Just as a tenuously related aside: during the last spell of snowy weather here in the south of England, a little girl wrote into BBC Radio 4 noting that in downhill sled races between her and her granny, her granny always won. She reckoned it was because her granny was much heavier. This provoked a flurry of emails from smartarses quoting Galileo trying to shoot the little girl’s theory down in flames. This in turn provoked a few more emails defending the kid’s theory, which was in fact correct. This was because although granny would be subjected to increased wind resistance due to her greater frontal area, her terminal velocity (achieved when wind resistance and friction effects exactly cancel out the pull of gravity) was higher, as losses due got greater frontal area were more than compensated for by granny’s extra mass.
I’ve noticed this effect myself, albeit on a bicycle. I’m tall and heavy, and coasting downhill I will easily outpace someone who is short and light. Swings and roundabouts though, as I’m at a disadvantage when having to go uphill…
Whaaaaaat? There’s no way the bolded part is true. If you have a downslope and then an upslope, you’ll beat the flat-biker’s time quite handily. This is because you’re spending more time going faster than V0. The slopes look more like the brachistochrone, which is the absolute fastest path from A to B with respect to gravity, and thus why they’re fastest.
This is where you err. Yes, the downslope time and the upslope time will match each other, but that doesn’t mean the times will match the flat biker going the same distance.
NB: Don’t confuse the brachistochrone, which deals with positive and negative acceleration, with headwind/tailwind/river current problems, which deal with additions and subtractions to velocity.
The answer to the OP has nothing to do with wind. It’s simple math…he’s slowed for a longer time on the uphill part and “runs out of downhill” before he’s spent enough time making up for the delay. This is true even in a vacuum.
It’s infinity. Infinity miles per hour. (To average 60 mph, the 2 mile course should take two minutes. However, at 30 mph it took two minutes to travel just the first mile, so there is no time left)
