Long Distance Competition/Ultracycling, Randonneuring and Endurance Cycling - Average speed

I mentioned to a friend that on a particular route I was slow climbing the hills.
I said that although I was doing 20 km/hr on the flat, I was riding only 5 to 8 km/hr up the steep hills.
He said, "It doesn't matter how slow you go up a hill because you can always make up for it on the downhill so that it will even-out your speed."
While his "theory" sounds plausible, it seems to me that in practice it doesn't hold up.

Can you comment?

It doesn't hold up because when you descend, your potential energy is
lost due air friction. Air friction force is proportional to the square of your
speed. So the faster you descend, the worse^2!! :(

Measure your time over a given distance that includes up/down and test the theory. I think it would be true for me. I cruise about 11-12 mph on my bike (heavy Hybrid with bags and lots of stuff) and typically drop to 6-7 mph on the up's but often run about 20-24 mph on the down side if I do some peddling.

For example:
2 miles at 20mph = 6 minutes. (2/20 x 60)

But going up a mile takes too long:
Up 1 mile at 10mph = 6 minutes.
Down 1 mile at 40mph = 1.5 minutes.
Total 7.5 minutes.
Going up slower would be worse. And even 100mph downhill wouldn't help.

If you went up at 13.33mph (4.5 minutes) and down at 40mph, you would break even.

I mentioned to a friend that on a particular route I was slow climbing the hills.
I said that although I was doing 20 km/hr on the flat, I was riding only 5 to 8 km/hr up the steep hills.
He said, "It doesn't matter how slow you go up a hill because you can always make up for it on the downhill so that it will even-out your speed."
While his "theory" sounds plausible, it seems to me that in practice it doesn't hold up.

Can you comment?

It's false, because you spend much more time riding slowly than you do riding quickly.

If you go up a half-mile climb at 10 MPH, it takes you 3 minutes. If you go down it at 20 miles per hour, it takes you 90 seconds.

Your overall time is therefore 4.5 minutes for a mile, which gives you an average of....

13.3 MPH.

I think you need to measure it yourself. After 1,000 miles of riding with my Garmin Edge 305, I can confirm that on hilly rides I average about 5 - 9% faster than on flat ones.

I live near a rail-trail that's very nearly (but not completely) flat. It drops about 200 feet in 11 miles one way, and I always go out and back. It's flat enough that there is no coasting - you pedal all the time.

My other rides are loops in slightly hilly central Massachusetts. I may slow down to 9 - 10 MPH on the uphills in spots, but hit 35 - 37 MPH on the downhills. If I went up a half-mile hill at 10 MPH I would be going a heck of a lot faster than 20 MPH coming down that same hill! All courses are loops ending at the starting point.

On downhills you also have the opportunity to coast and rest a bit, too.

I have ridden about 600 miles of hilly courses and about 400 miles of the flat rail trail. My overall flat course average is 16.4 MPH, and my overall hilly course average is 17.5 MPH. So I'm almost 7% faster on the hilly rides. I suspect that's small enough to be dominated by individual style/performance so I would guess that some folks are faster on the hills and some are faster on the flats.

For example:
2 miles at 20mph = 6 minutes. (2/20 x 60)

But going up a mile takes too long:
Up 1 mile at 10mph = 6 minutes.
Down 1 mile at 40mph = 1.5 minutes.
Total 7.5 minutes.
Going up slower would be worse. And even 100mph downhill wouldn't help.

If you went up at 13.33mph (4.5 minutes) and down at 40mph, you would break even.

+10
Also, the physics momentum you're supposed to get back going down is absorbed by air resistance, and more importantly, the practicalities of braking.

Basically, you spend 2 hours climbing this hill at a snail's pace, but only 5 minutes flying down this same hill. You'll never make up for the lost time spent climbing that hill........time being the major variable in calculating average speed.

Do you go down hills 24 times faster than you go up them? :rolleyes: If not, then your math isn't helpful. We can all invent numbers. I think it would be helpful if other posters with actual personal data (real experience) could post them, too. We're all able to make up numbers to prove our points.

For example, if I can cruise 20 MPH on the flats, slow down to 15 MPH on a 1-mile uphill, then come down that 1-mile downhill at 35 MPH, guess what? I did those two "hilly" miles at an average speed of 21 MPH - about 5% faster than the flats.

I suspect that gentle, rolling hills may produce a different result than huge ups and downs. And your gearing and ability will matter, too. So I'd certainly like to hear real data from other riders - thanks!

I mentioned to a friend that on a particular route I was slow climbing the hills.
I said that although I was doing 20 km/hr on the flat, I was riding only 5 to 8 km/hr up the steep hills.
He said, "It doesn't matter how slow you go up a hill because you can always make up for it on the downhill so that it will even-out your speed."
While his "theory" sounds plausible, it seems to me that in practice it doesn't hold up.

Can you comment?

Not exactly true: The fastest average speed you can attain on a climb and descent is twice your climbing speed. Suppose you ride up a one mile hill at 4 mph, so it takes you fifteen minutes. Now turn around and ride back down at an infinite speed so the descent takes precisely zero seconds. Then you've ridden two miles in fifteen minutes for an average speed of 8 mph. So you've "evened-out" your speed somewhat, but there's a limit to it. That's partly why the TdF guys who are fast in the mountains win the Tour.

Hills are one aspect of cycling that proves that "weight" matters. The other aspect of cycling that hills prove is that "power" matters. When climbing speeds fall well below your current "average" speed, the kind of speeds necessary to regain "average" become unobtainable. To see just how critcial it is to maintain pace - do a few more math problems subbing in 6mph for 8mph. Just 2mph difference on a half-mile hill........

6mph for a half-mile - 5minutes requires == 18mph for 4.3 miles to regain 15mph
8mph for a half-mile - 3min 45secs requires == 18mph for 2.4 miles to regain 15mph
12mph for a half mile - 2min 30secs requires == 17mph for 1 mile to regain 15mph

EDM, you're comments are too goofy to refute. But no one rides more efficiently on hills. And the idea that "on a hill" you can manage 15mph while climbing - will "give back" 35mph on the downhill is ridiculous. And even if it did, it would not be for a very long period of time or distance. No one "gets" 35mph payback or a grade that only slows them to 15mph.

15mph for a mile - 4mins == 30mph for an entire mile to regain 20mph, not likely, since at the top of the hill you are starting from 15 mph. More likely you would need 24mph for two miles. Even if you were on perfectly smooth road and riding in a vacuum it would take more power to crank up to 35mph.

Do you go down hills 24 times faster than you go up them? :rolleyes: If not, then your math isn't helpful. We can all invent numbers. I think it would be helpful if other posters with actual personal data (real experience) could post them, too. We're all able to make up numbers to prove our points.


Those were arbitrary numbers I picked out of thin air just to illustrate a point to show people who're not into numbers and formulas. I hope it made some sense to the OP....:)

Edit: Although I picked those numbers out of thin air, theoretically say someone on a trike winches himself up a steep climb at 2mph and descents back down at 48mph.......now that is possible...:D

Another way to look at it.

Downhill 1 miles at 60 mph = 1 minute
Uphill 1 mile at 1mph = 1 hour

Total Miles: 2.0
Total Time: 1 hour and 1 minute.

Average speed: 1.98 mph

Ditto that it is a false assumption, for the reason already stated: you spend most of your time climbing and very little descending. In addition, your descending speed is going to be more of a constant. Notice how on a long descent you reach a certain speed and stay there? That's based mostly on your mass, wind resistance, and slope. A given rider on a given bike will usually top out around a particular speed, once the wind resistance balances out with the gravitational pull. However the speed of the climb is what will change your average speed since your descent is more or less constant.

Well, in actuality your climbing becomes more or less a constant too, but you can increase it significantly with a greater effort, whereas a greater effort on the descent yields you hardly anything...

Here's somthing to read...

http://www.sportsci.org/encyc/cyclingupdown/cyclingupdown.html

my average speed is always down on rides with big climbs... for example the ride I've got planned Monday is about a 140 miles with two 'decent' climbs... for those of you familiar with Vermont they are rt 108 south from Jeffersonville to Stowe going over Smugglers Notch and rt 17 west from Waitsfield to rt 116 in Starksboro going over Appalachian Gap... the Smuggs climb gains almost 1800' and App Gap gains probably 1600'...

my average speed will be about 1-1.5 mph slower than 'normal'... normal being a ride with plenty of climbing but in the form of rollers... the descents will not even out the two climbs!

Since I originally posted this question, let me add another ingredient.
First of all (as demonstrated by several posters), mathematically the overall speed is not "evened out"
However, if I am riding at 20 km/hr along the flat, just before the rising hill, my speed does not decrease until I am into the hill.
However, once I am at the crest of the hill, my speed is back to 20
Then I pedal like a mad-man so that my speed increases to 50.
But when I reach the bottom along the flat, my speed for some distance is well above 20.
Does the increased speed at the bottom help to "even out" my average speed?

In practice, on a hilly route of 42 km, my overall average is 20 and yet along the flat I am doing 20.
Yet going up the hill I am doing only 10.

How is this possible?

Probably the easiest way to understand why hills alter cycling efficiency is this:

All the energy you "store" by climbing a hill and overcoming gravity is "released" when you go down a hill to the same altitude at which you started climbing.

However, while you were climbing you also had to produce energy to move through "air". The only way a hill could begin to give back the same amount of energy downhill as when you climb would be by "giving" you a tailwind above the speed at which you descend. If you slow down 10mph on the hill, then you need at least a 10mph tailwind ABOVE YOUR CURRENT SPEED going downhill just to break even!

The "big deal", is that the ability to climb at just 1 or 2 mph difference returns an incredible amount of distance or speed on the downhill. Anyone who has ridden a hilly route with good riders, knows just how this works out - when amplified over 100 mile ride. Those guys are already gone and at home showering while you're 15 miles from the finish.

Pedalling like a madman burns up a lot of energy for a little return. Over the summit of a climb, yes, briefly ratcheting it up thelps get to descent speed a little mor quickly, thus gaining a few seconds...that is all. After that, let gravity take over and work on your form descending for greatest efficiency. IF you are in the middle of a descent and have leveled out to, say 40 MPH, and you hit the cranks hard to get to 43-45 MPH and stop pedalling, you will level back out to your previous 40...assuming the gradient is reasonably consistent.

The reason being that mass and wind resistance find an equilibrium much as a skydiver would on a free fall. If you are racing and need a few extra seconds for a gap, you might spend that energy. Otherwise those few seconds really don't change your average speed, so you are best saving that energy and recovering on the descents so you can spend it on the next climb.

You will gain more time on a descent by exercizing good form than you would pedalling like a madman...

To illustrate...my lazy form on a descent usually yeilds me about 40 mph, and my efficient form gets me about 45 mph.

The riders in the TDF averaged significantly faster speeds on the level stages as compared with the mountainous ones. On the level ones they were often averaging 27-28 mph. On the mountainous ones they were averaging closer to 20 mph - some were even below 20 mph. Also, on the flats the riders for the most part all stayed together, whereas in the mountains huge time gaps opened up and some riders (memorably Tom Boonen) had to drop out.

To answer the question of which is faster, consider an extreme example. Suppose you were riding a 100 mile course where you first rode 50 miles up a mountain and then 50 miles down. Suppose going up it was so steep you could only average 5 mph. It would take you 10 hours to ride this first half. Even if you could somehow (impossibly) do the descent instantaneously, your century time would still be 10 hours - not too good. In all likelihood you'd be able to do a flat century much faster than the 10 mph average you would have attained on this mountainous course. Basically, just mentally picture a course with a hill so steep and long that you could barely move up it - there is no way that descending that same hill again could possibly regain all of the time lost on the ascent.

I think the absolute true test is to ride on hilly terrain and compare the distance and avg. speed to riding on flat terrain. There are a lot more factors involved then simply the speed uphill vs. the speed downhill.

I live in a hilly area and average around 16 mph on a 20 mile course.

I recently went to work at a client in Indianapolis, which couldn't be flatter. So, now I ride there during the week. My average went up to 22 mph over a 20 mile course. This includes stops of which there are a lot more of around Indy then back home. I probably would get a more accurate comparison if I removed the stops from the readings.

To answer the question of which is faster, consider an extreme example.
The problem is that that doesn't answer the question. It just throws together a set of extreme, hypothetical numbers that have no relevance to the real world. As we've seen earlier in this thread, one can also invent numbers that "prove" the opposite.

Too many people sitting around in front of the computer typing instead of getting out there, riding, and reporting some real data;)

The riders in the TDF averaged significantly faster speeds on the level stages as compared with the mountainous ones.

Yes, but that's irrelevant to this discussion because the mountain stages in the TdF are uphill. They don't get to go DOWN L'Alpe d'Huez, do they?

All of the five mountain stages in this year's TdF ended at a higher elevation than they started. In total they ended over four kilometers higher than they started! Only two of them even come close to being level:

Stage 10 - start 79m, end 202m
Stage 11 - start 325m, end 1830m
Stage 15 - start 785m, end 1850m
Stage 16 - start 716m, end 1705m
Stage 17 - start 484m, end 975m

Measured by the winning rider's speed, the two fastest stages in the 2006 TdF (outside of the ITT and prologue) were the decidedly NON-flat stage 12 and stage 18; the two "out-of-the-mountains" stages that dropped about 500m and 800m respectively from start to finish.

The slowest speed for a winning rider? The rather flat stage 2!

Too many people sitting around in front of the computer typing instead of getting out there, riding, and reporting some real data;)

Here's my real data. I just finished the Seattle Randonneurs 1000k brevet, which went over three mountain passes. The first day we went over Stevens Pass, and I did the last 8 km of climb in exacly one hour at 8 km/hr. On the first few km of descent I was doing close to 60 km/hr, which means about 8 minutes to do the first 8 km of descent. Total time for 16 km: 68 minutes, 14.1 km/hr average. On a flat stretch of road, I would usually average twice that speed, about 28 km/hr.

I'm not a big MPH junkie but on smaller hills, I tend to do my greatest MPH. Maybe it's because I keep up my normal pedal rate when climbing up a small hill while I can still go fast down a small hill.

But on steep hills, my MPH drops like a stone in water.

Flat land I ride about 21Mph. Climbing most hills I ride about 12-14 Mph, Descending I ride between 30 and 50 Mph, depending on the hill.

What does that all average out to? I dunno. I just thought I would share.

Now this has been raised from the dead...

I discussed this subject briefly with with Pierce, the technical director of the Boston-Montreal-Boston, and a man who has a LOT of experience coaching riders in RAAM. He made an interesting observation -- that the course for RAAM was altered specifically one year to be flat (ie, with only a small amount of mountain climbing) to try to encourage a record finishing time to help promote interest in the event. The first rider crossed the line in a time SLOWER than in previous years. Of course, all sorts of ambient conditions may have played a role in the slower time. But I figure that maybe riders can sustain only a certain maximum speed on the flats over long periods, especially when they are riding by themselves and without drafting assistance.

Incidentally, BMB is considered one of the hilliest randonnees out there (guesstimates of climbing range from 40,000 to 54,000 feet). I am not sure of the exact record finishing time for the event, but I think it is about 47 hours. PBP is somewhat less hilly (claimed to be around 33,000 feet I think), and the record there, I think, is around 44 or 45 hours.

Based on some of the THEORY contained in this thread, anyone riding BMB wouldn't have a chance in hell of finishing anywhere near the PBP time, let alone only three hours outside the PBP time. That is, for ~33% more climbing on BMB, the finishing times are only ~2% apart.

And it should be noted that the PBP times have been skewed by large pelotons of riders drafting along as TdF cyclists do, on relatively rolling roads. I did not see more than eight or nine rides in any group on BMB-2006, and when Saunders Whittlesey set the BMB record last year, he did it almost entirely as a lone rider. Interestingly, for the Last Chance, which is one of the flattest 1200 randonnees out there... no rider in the past three years has broken 50 hours... indeed, 53 hours.

I am not saying that the original premise is correct or not. I do think, however, this is another case of theory standing in the way of practical experience. Theory ALWAYS works in ideal conditions... ideal road surfaces, ideal straightness of the road, ideal physiology of the rider, ideal frictionlessness of the bike, ideal ambient conditions, ideal peloton conditions. Practice very rarely delivers up those ideal conditions. I also bet that the comment to Cadillac was made in the context of non-competitive, non-high-performance riding.

...

Incidentally, BMB is considered one of the hilliest randonnees out there (guesstimates of climbing range from 40,000 to 54,000 feet). I am not sure of the exact record finishing time for the event, but I think it is about 47 hours. PBP is somewhat less hilly (claimed to be around 33,000 feet I think), and the record there, I think, is around 44 or 45 hours.

Based on some of the THEORY contained in this thread, anyone riding BMB wouldn't have a chance in hell of finishing anywhere near the PBP time, let alone only three hours outside the PBP time. That is, for ~33% more climbing on BMB, the finishing times are only ~2% apart.

And it should be noted that the PBP times have been skewed by large pelotons of riders drafting along as TdF cyclists do, on relatively rolling roads. I did not see more than eight or nine rides in any group on BMB-2006, and when Saunders Whittlesea set the BMB record last year, he did it almost entirely as a lone rider. Interestingly, for the Last Chance, which is one of the flattest 1200 randonnees out there... no rider in the past three years has broken 50 hours... indeed, 53 hours.

...



Theory:
Assume BMB is a 750 mile long climb.
Assume 40,000 feet of gain.
Thats 53.33 feet per mile.
According to CycliStats climbing calculator that is a 1% grade. Nothing really. :D

If we say BMB is 33% flat, 33% climbing, and 33% descending the gradient jumps up to an average of 3.06%

If we say PBP is 33% flat, 33% climbing, and 33% descending the average grade for PBP is 2.53%


Looking at BMB vs PBP: (and lets use the assumed record times and just do the math)
Assume that a cyclist going for a record would be highly skilled at climbing - essentially climbing at the same rate in either event, even on the steeper grades of BMB.

PBP - 33,000 feet of climbing
44 hour ride time
Average Speed (total): 17.04 mph
Climbing 750 feet per hour

BMB - 40,000 feet of climbing
Assume you climb at the same rate as on PBP - 750 feet per hour
This yields a ride time of 53 hours 20 minutes - much higher than the record for BMB.
Average speed drops to 14.06 mph

The PBP time is 82% of the BMB time.


Or:
To finish BMB in 89:59 you must climb 445 per hour, and have an average speed of 8.35 mph.
In order to finish PBP in 89:59 you must "only" climb 367 feet per hour, traveling at the same speed.

If you climbed PBP at the rate you climbed BMB you'd finish PBP in 74:09, which is 82% of your BMB time.


Practice:
Your numbers above show a PBP time of 93% of BMB time. (44/47)
Theory:
PBP in 82% of BMB time.


This is an 11% difference from theory to practice. (82% vs 93%)




So, people appear to be riding BMB faster than PBP.
Why?

Lots of rollers with a large group may be inefficient.
Thousands+ cyclists (perhaps quite a few of them not attempting a record) on the roads may overall be slower than 100. Or 1.
Individuals descend faster than groups - and BMB has some long descents (and this is not related to average speed as we've been talking - only in that on average a single rider or a small group will go downhill faster than a big group - and my guess is this is more true at night, in the rain, etc.)
PBP controls are packed, until one gets out in front of the peloton.
From what I've read, PBP has spectators out and about selling goods and food along the way, whereas BMB can be pretty desolate going over the mountains and in Western Mass. Perhaps BMB riders are hungry and rush to get finished? Or PBP riders enjoy the hospitality and the wine and pastry?




Or we can look at it this way:
France has a 35 hour work week. (PBP)
The US has a 40 hour work week. (BMB)
Your PBP time will be 87% of your BMB time following this formula.
Not quite the 93% as above... but a happy middle ground between theory and practice. :D




My point? I don't have one.

Its late. I needed to work off my coffee and driving buzzzzz.
Math makes me sleepy. :crash:

Or we can look at it this way:
France has a 35 hour work week. (PBP)
The US has a 40 hour work week. (BMB)
Your PBP time will be 87% of your BMB time following this formula.
Not quite the 93% as above... but a happy middle ground between theory and practice. :D



Nice breakdown...especially the above section. All kidding aside, there's at least a few ways to run the numbers to get vastly different answers. I'm planning on going to PBP this year, and I never considered that folks would be selling wine on the route. Perhaps I'll have to re-calculate my projected time between controls ;) .

Dead thread but I can't resist....

Let's say you have a 10 mile ride with one high point. It's a 5 mile climb up, and a 5 mile decsent down, even grades. You go up the hill at an average speed of 5 miles per hour. That's 1 hour to get up. You come down at 20 miles per hour. That's 15 minutes to get down. Total time is 1 hr. 15 minutes to travel 10 miles. Average speed is 8 miles per hour. Reason it matters is that you spend a far greater amount of time to go up, and average speed is speed/time.

The ride that I do has 3 options of terrain that I can sort of mix and match, depending how I'm feeling on a given day. I can do big hills if I head Southeast, flats if I go straight south, and rolling hills if I go southwest. I do my rides in a loop, so these roads all intersect so on the way back I am able to choose terrain for the way back, based on how I'm feeling also. So I've noticed a couple of things.

1. The big climbing route yields the lowest average speeds. When I get to the point where the 3 routes intersect when I'd been on the big hills, my average has never been much higher than 17.5 mph.

2. If I take the flat route to get to this same point, my average speed ends up around 20-21 mph.

3. I've only taken the rolling hills route out to this point once, and I can't remember what my average speed was to get to that point... so sorry, no data for that.

My best effort on the big hills then rolling hills route has been 19.6 mph, and I worked real hard for it. If I stay on the flats I am able to keep my average speed over 20 mph without nearly as much effort for comparable distances, though I've never made a huge effort on the flat to see what would happen if I went all out. So suffice it to say that I personally am not faster in the hills, and but then again my "flat" is relative, being from NH, it is nothing like what someone from Florida would call flat.

Hi. I know this topic has been thoroughly discussed, but I'd been thinking about it as a mathematical problem and I came to an insight I'd like to share.

Averaging over time, your average speed is the arithmetic mean. Averaging over distance, your average speed is the harmonic mean.

Suppose you ride for three hours, going 12mph the first hour, 20mph the second, and 15mph during the third. Then your average speed is the arithmetic mean of 12, 20, and 15: (12+20+13)/3 = 15mph.

Suppose instead you ride three miles. During the first mile you go 12 mph, the second 20, and the third 13. Then the average speed is the harmonic mean: 1 / ( ( 1/12 + 1/20 + 1/13 ) / 3 ) = 14.27mph.

Thank you for your attention.