In theory what is more efficient?

IF you go through terrain varying in altitude up and down, is it more efficient to put most effort in climbing than stop peddling on the downhill? Or just stroll(go up slowly) the hills and ride fast down hill?

Also if you arent riding what is the most comfortable foot position is it wher the pedals are at the same height as eachother?

For me often I will climb fast uphill and put no effort downhill because I know Ill be stopped by traffic or find it too dangerous to go that fast.

As a purely practical matter, increasing your speed by a few mph on the way up will save you more time than increasing your speed by the amount on the way down.

I wouldn't really see a benefit in really putting an effort going downhill, since gravity is helping you anyways.

I would climb like no ones business and aerotuck it all the way down the back side gives you a chance to rest and hydrate

I vote for pushing hard up the hill, it seems like if you slow down on them, you end up pedaling just as hard, but in a lower gear.

Put the effort into climbing and coast on the downhill. On my commute I have too many stops going downhill to bother pedaling anyways.

Laws of Thermodynamics pwns joo! Put your effort into climbing and rest on the down hill.

I do both but tend to haul arse going up hills. There is nothing quite like a little hill training to liven up a commute.
I have a steep hill that I head down in the morning. It's too freaking hard to resist seeing what speed I can hit going down it.

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Both!!!

Both. I like going fast on the downhills, but I still shift to the highest gear ratio that the bike has and I pedal.

As Sheldon Brown says about fixed gears: "Coasting breaks up your rhythm and allows your legs to stiffen up. Keeping your legs in motion keeps the muscles supple, and promotes good circulation."

https://sheldonbrown.com/fixed.html

Same idea here, it's just that I put a lot more effort into the climb, since gravity works against you there.

+1 The ascents burn up so much time esp. on the long ascents.

Depends on what you mean by 'efficient'.

Are you trying for the best times? Are you racing? In a hurry?

Or are you trying to conserve energy?, or pace yourself?

Concerned about bonking?

Trying for the easiest or most pleasant approach?

Trying to make the most miles?

Just curious?

Or?

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Also, it seems that it would also depend in part on the nature of the hills. If they are not too bad, it could be very good exercise to turn them into intervals.

The length of the trip would also factor in, and your fitness level.

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If you sense a safety issue in going too fast on some of the downhills, it is probably not worth risking your life or your health to save a few minutes or seconds.

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You can chart it. It tends to make things clearer. (When I did this, I was surprised by the time factor -- when you are going very slowly, the time factor really skews your average speeds and overall times.)(You can also try it several different ways, and time yourself. Many cyclocomputers, even the inexpensive ones, can also help in nailing it down; but you can also just time it....)

It all depends upon the hill.

It does depend on the situation, but if you want to go fast without wasting effort then you should definitely follow these rules:

If you're going to want a time to take it easy, take it easy on a downhill rather than before or after. If you're going to pick a time to pedal your heart out, do it on the uphills. The reason is that it takes more total energy to go 100 meters at a high speed, than to go the same 100 meters at a slow speed.

A perfectly even speed would mean the smallest loss of energy due to air resistance, and dramatically-changing speeds (pedal hard downhill and be lazy on the uphill) are likely to lose you a lot of energy to air resistance.

Going exactly the same speed all the time usually isn't a perfect strategy because your body probably works most efficiently with fairly small changes in your effort level. Pick up your effort a little on the uphills and relax on the downhills and you may find it easier to make a fast trip overall.

Also, on multi-speed bikes it's best to gear down and spin the pedals faster when you're putting in the most effort (uphills) and gear up to make the pedals move slowly when you're not working hard (downhills).

If you crank 150 watts going up, and 150 watts going down a 1/2 mile hill, you will arrive at your destination later and use more calories than if you cranked 300 watts going up and coasted down.

Okay, everbody else answered the uphill/downhill thing, so I'll do the pedal position thing.

Are there curves on this hill? If there are, your bike will be more stable and get better traction if the pedal to the outside of the curve is at 6 o'clock and the majority of your weight is on that foot.

Power is proportional to the cube of speed. This is primarily due to wind resistance. So, it takes way more power to go from 20 to 21 MPH than it does to go from 4 to 5 mph. If your ride has the same amount of uphill as it does downhill (such as a round trip route), then you're better off putting your power into the slower speed segments (uphills).

But that rationale makes lots of assumptions. For example, it assumes that you have a fixed amount of total power (energy) to deliver during your ride, and that you can apply power at any rate. In reality, the amount of power you can provide depends on the rate it is provided (slow and steady wins the race), and there is obviously a limit to your peak power output.

So, when you're talking about the bike/body combination, maximum efficiency is more related to the relatively narrow range of efficient power production of your body. In other words, find the rate of power delivery that you can (or want to) sustain for the duration of your ride, and stay close to it, regardless of incline.

+1 depends on how much weight in my pannier as to how fast I want to descend...

You'll want to spend your effort going uphill.

I'll explain using an example. The numbers are made up, but calculated according to real-life principles and laws.

Assume a course 10 km long. The first 3 km are flat. The next 2 km are uphill at a 6% grade. After that, 2 km downhill at 6%. Finally 3 km flat.

Our fictional rider has a constant 200 W at his disposal.

For the first flat part, this gives a speed of 31.1 km/h for this fictional rider. The 3 km takes 5 m 47 s.
Our rider hits the hill, and his speed drops to 13.5 km/h. The hill is eaten up in 8 m 52 s.
Passing the summit, the speed instantly increases to 53.5 km/h. Time downhill is 2 min 15 s.
The final flat part is equal to the first.

Total time, then, is 22 m 41 s. Much of that time is spent going uphill.

Let's say our rider coasts downhill instead, but rides the same way on the flats and uphill. He still rolls downhill at 46.2 km/h and takes 2 m 36 s to do so. The course then takes 21 seconds longer to complete.

Now we give our rider 100 W extra to spend on either one flat part, the uphill part or the downhill part.
If the 100 W is spent on one flat part, the total time decreases by 50 s to 21 m 51 s.
Spent going uphill, time decreases by 2 m 35 s, for a total time of 20 m 6 s.
Downhill at 300 W instead of 200 W, time saved is only 7 s! Total time becomes 22 m 34 s.

I'd guess that in the above example, the rider could avoid losing those 7 s downhill by coasting and going into an "aero tuck".

This is an easy question. I go slow uphill because I can't go fast uphill. I coast down the other side because I need to rest after making it up the hill.

Im looking to conserve energy. I only have to ride 2km each way. takes me about 10-15 minutes Id guess. Because I dont check the time leaving my house and entering buildings.

Jeez...........I wish I could ride fast uphill.