# Uphills and downhills vs a flat

I started the debate with my brother asking him, "If you had to do a 20km ride around a circle I.e at the end of your ride you arrive at the same place you started, would you rather cycle on a flat or have uphills and downhills to get the best time?" To this he answered "I would rather cycle on uphills and downhills, mainly because I have time to recover on the downhills." I said that I'd rather go on a flat because you burn out faster on the uphill than you recover on the downhill since the time spent going down is considerably shorter. Id like to hear from the community on which side of the debate they stand and why.

Note: someone please edit my tags I have no idea which to use.

• The problem as I see it is that assuming equal uphills and downhills, you will have less time to recover than you will spend out of the saddle. I guess it depends how steep the hills are among other things, but if the hills are quite steep, you will spend much more time ascending the hill then riding the gravity on the way back down. If it was a question of tailwind and headwind vs no wind, I could see some logic to it, but for hills, I just can't see it evening out. Also, on very steep hills, once you burn out your muscles, no amount of recovery can help in the time span of a ride. Commented Jan 12, 2015 at 14:55
• Because wind resistance is not linear (velocity squared) flat is more efficient. Commented Jan 12, 2015 at 15:38
• In terms of total energy expenditure the flat course is more "efficient". However, the human body is not always most efficient when running at a fixed pace, but benefits (if only in terms of less boredom) from a little variation. As to the wind, my experience is that the only time you ever have a tailwind is when climbing a steep hill on a warm day. Commented Jan 12, 2015 at 20:25
• There is one thing that will be different in flat and up/down hill... "Momentum"... How it will affect the time (either gain / loss) will depend on the height of the up / down slopes and distance. Commented Jan 15, 2015 at 3:43
• Efficiency is a measure of energy delivered to the cranks as a proportion of energy metabolised. Talk of speed, wind, hills etc are not particularly relevant wrt efficiency. High power supra threshold efforts (such as powering over a short climb) that tap limited anaerobic energy pathways are most definitely not efficient as their purpose is to provide energy rapidly, not efficiently. Commented Jan 15, 2015 at 11:13

This question explains that if you travel on uneven ground, your average speed drops. This is because you spend more time in the slow climbs and less time in the fast descents.

I know you are going to doubt this but the average of 10 and 30 is 15.

Assume a 30 mile ride at 15 mph for a total of 2 hours.

Now 15 miles uphill at 10 mph for 1.5 hours and 30 mph downhill for .5 hours for a total of 2 hours.

Wind resistance hill versus flat
c is constant
a is frontal area
Wind resistance is proportional to the velocity squared

``````(1.5 * c * a * 10 * 10) + (.5 * c * a * 30 * 30)
/
2 * c * a * 15 * 15

=

(1.5 * 10 * 10) + (.5 * 30 * 30)
/
2 * 15 * 15

=

4 / 3
``````

Just to achieve the same net time you would expend 1/3 more energy on wind resistance with split speeds

Energy to climb up and down the hill is a wash

The same wind resistance as the split the flat could be about 17 mph.

Drag (physics)

• Come on why the down vote. Really ask a question or comment. I have a degree in engineering - that analysis is accurate. Commented Jan 13, 2015 at 13:55
• No idea why someone down voted this. It could be a little clearer to read but that's a minor quibble on an answer that works through the maths that i couldn't be bothered to do. +1 from me. Commented Jan 15, 2015 at 10:51
• Yeah we don't have the formula extensions that some other stacks have. Might be better to do the maths as an image and put that in-line.
– Criggie
Commented Apr 29, 2016 at 4:38

The optimisation of speed for a given course profile, environmental conditions and rider's physiological capability is a multi-variable optimisation problem. Factors include:

• the physics of cycling, with the proportion of energy demand from the various resistance forces varying depending upon gradient and wind conditions, as well as a rider's morphology, and that the speed vs power relationship will vary from a mostly cubic to a mostly linear relationship or a mix depending on the those variables.

• the physiological capability of the rider

• the fact the physiological cost of riding is curvi-linearly related to power output, i.e. an increase in power comes with an even greater physiological cost. Put simply, riding at a handful of % above TT power and you'll fatigue very quickly, but ride a handful of % below TT power and you can sustain that effort for a very long time

• The result of this relationship between the physiological cost and power output is that the more variable a rider's power output (e.g. to power up climbs and recover on the descents), the lower the average power of the rider must be. IOW you cannot assume you are capable of attaining the same average power if you choose to increasingly vary power output over a given course.

• In addition, you can't ride much harder than what your mean maximal power capability is for the entire duration for any more than short periods

When you properly consider all of these factors, and it's possible to quite effectively model them, then you'll realise the fastest times for a given distance on courses that begin and end at the same location will always be for flat routes with very low or no wind conditions.

Alternatively you could just investigate time trial results from decades of competitions are see what sort of courses provide the fastest speeds.

The fastest rides will inevitably be from flat courses with some form of reduction in air resistance, either due to traffic flowing in the same direction as the rider, and/or because they are at altitude. Hillier courses do not feature in the history books as providing the fastest speeds.

Then of course the world hour record is set on a velodrome which is of course a short loop providing a never ending flat circuit.

Isn't standing out of the saddle for a hill less efficient than riding on the flat (assuming someone less than a seasoned pro)? Sheldon says so. If so the average efficiency is worse on the hilly route and for the same input it would be slower. Of course as the hills become less steep the efficiency tends towards the flat case - there may be some sweet spot but on the whole I doubt it. Also drag is an issue - on a circular flat route in constant wind you will lose to headwinds more than you gain from tailwinds. A detailed treatment of the wind effects by Osman Isvan is worth a read. Applying the effects of the headwind caused by riding to a route of alternating uphill (slow) and downhill (fast) sections, and given that the power lost to the wind goes with the cube of the speed you will again lose more power on the fast stretches than you gain on the slow.

I've only approximated the maths in my head but would conclude that a flat route is better.

Apparently you should even consider slope wind.

I think the trainer Frederic Grappe (FDJ team) had a good answer. He would rather an uphill and downhill into the wind than a flat into the wind because you would waste more effort battling the wind compared to the hill.

Otherwise on a circular course flat will be quicker due to frictional losses on the slow climb and increased wind losses on the descent.

It depends on the how steep the hills are and how long they are.

In theory, riding on the flat should be faster. But in my experience undulating terrain is the fastest. Let me explain.

Using maths you can easily see that what effects your time over a course (hence your average speed) the most is how long you spend at lower speeds. So to set a quicker time we should improve our time on the slowest sections first.

If the road is flat then that is hard. When the hills too steep and long it is hard also.

But when the hills are short enough that I can power up them, then with extra energy expenditure I can maintain a good speed. This is psychologically aided by being able see the top and know the effort is short term.

Then, after passing the crest, comes the important bit, and this is why the hills have to be short and not too steep: apply power on the way down also.

If the downhill is followed by a flat section then by maintaining the effort level that speed can be maintained for many minutes. But if the downhill is followed quickly by another short hill, then the speed can be used to attack the next hill.

So too steep and long means too steep to climb quickly.

An example is a long shallow climb I do here. It averages only about 2% and so I can ride at about 25kph. Then I come to a 600m section which descends at over 7% then climbs at over 9%. Overall, the section rises at an average of 5%, but I average 32kph.

It's psychological.

In theory flat. Also if you think about it downhills are more for your bigger gears. It is best to not recover but catch speed as your goal is speed. At least for me climbs require a lot of effort and if you add the effort of going on biggest gear on down hill it is actually mean you are less efficient as if you where going on flat road.

Quite thin argument, I know, but these climbs will destroy the advantage that downhill give you.

From the practical point of view, you will get more tired on ups and downs, but more bored on flat. Downs do not compensate for ups, because they require a lot of concentration and muscle power - your speed is much higher on downhills! You will be very tired after a 30 minute downhill, which never happens on 30 minute flat. In fact, roads where there's very little flat and mostly hills are very hard to ride physically although fun for your mental part.

Never really bothered calculate it, but emprically on long rides my normal daily distance on flat is 180-200 km, in the mountains 120-140 km. This makes it obvious on which one is more "efficient" distance and speed-wise.

On the other hand, ups and downs are much more beneficial for your fitness.