(MTB rider here, XC & DH, with little road exp.).
There is a certain speed for which up to that speed you should pedal, above it you gain more from adopting the most aerodynamic position and use gravity the best you can.
In my case I find this speed by trial and error in specific circumstances, because it changes according to slope, terrain, bike and tires used and length of the descent.
What I have found is that once you get to the highest gear and start approaching your max cadence, it is very difficult to provide the power needed to accelerate, and it may be even harder to do so while tucked in aero position.
At this point, if the incline is steep enough, tucking in more will give you more advantage than pedalling.
In have one example, where a hardtail mtb with knobby tires on a paved road with little incline (I can ride it up at 20km/hr approx)
this speed is around 42 km/hr .
At this point I'm near max cadence in highest gear, so I adopt my aero position.
It is common for me to even overtake other riders who are pedaling and when I get to the bottom of the hill, I can pedal harder because I have had a rest during the descent.
In those descents, I get near 50 Km/hr just because of aerodynamics.
(In a road bike in the same road, my threshold is near the same, and i know/feel my speed in aero position is much higher, unfortunately I don't have the numbers yet)
This works for me because in my general shape and level of fitness, on MTB rides, if I stop and rest for 3-5 minutes I resume pedalling approx 5 km/hr faster than if I pedal continuously.
For longer rests my body starts to cool down
and I have to re-warm up.
And this is where descent length comes into place.
If the descent is long enough for you to cool down, (climate can have a role in this too)
then the benefit of the rest you get, is negated because once you get to the bottom of the hill you have cooled off and will have to warm up again.
For these cases, I recommend what some call "soft pedalling", that is pedal just to keep the blood flowing, sustaining the heart rate up.
This can be done at intervals, alternating between aero position and soft pedalling, according to your cool-off time in that particular descent/climate.
You need to find a certain speed threshold, a simple computer will do.
I know this is subjective, but there is a speed where you feel you need to put double the effort to get 1 Km/hr faster.
In that point tuck in aero position an watch what happens with your speed.
bicycles.stackexchange.com/users/2177/Jahaziel
Here's a good article from a man who knows a thing or two: Coast or Pedal on a Downhill?, Joe Friel Aug-10 Key thing from the article is reference to a 50-40-30-20-10 rule: Coast (and focus on getting aero) at
>50km/h Pedal easy at >40km/h Pedal steady at >30km/h Pedal moderately hard at >20km/h Pedal hard at >
10km/h
This lends itself more to racing against the clock (e.g. Time Trials and Triathlon) rather than a road race where staying with the bunch is important for the drafting effect of riding behind someone else.
The above "rule" is down to the fact that the faster you go, wind resistance increases and more-and-more energy is required to increase your speed by a set increment.
E.g. the difference in effort to ride at 20km/h compared to 10km/h is a lot less than, say, 40km/h compared to 30km/h. Check out the 'Drag (physics)'
on Wikipedia if you want to read more: drag is proportional to the velocity multiplied by itself (squared).
bicycles.stackexchange.com/users/13582/adey_888
I have no idea if it's efficient or powerful
but I do know that ever since I was a kid right up until now it is pure FUN to pedal as fast as I can, get as much speed as I can, and then see how far it it carry me.
Simple arithmetic.
bicycles.stackexchange.com/users/13747/Fujigirl
There's a few possible answers: 1, For racing
yes
but as Jahaziel says, you will reach a point where either the effort is too great to increase speed or actually you're just spinning out2, On a ride for fun or fitness there's no NEED to pedal downhill
but I find that if it's downhill followed by an uphill it launches you into the hill with more momentum which at least starts the climb better3, Obviously you might be trying to better a descent time in which case treat it like racing.
Obviously all this is dependent on the conditions, your skill and your experience.
bicycles.stackexchange.com/users/13410/atlaz
Because wind resistance is proportional to velocity squared it takes more power to go from 30 to 32 than from 15 to 17.
So you get more bang from your pedal power at lower speeds.
If it is a relatively short downhill
and you have considerable speed
you are typically better off coasting and then pedal when you get to a flat or flatter section.
You are better off exerting yourself on the lower speed ascent.
Then recover on the downhill.
It might be 2 minute recovery or 20 minute recovery.
If you notice racers typically go all out on the ascent.
If you went up the hill at 8 mph and down the hill at 13 mph compared to a constant 10 mph you would have about 5% more wind resistance.
bicycles.stackexchange.com/users/7785/paparazzo
How do I use up less when I go down the hill? What is better? If I really drive down (I start down the hill fast and when I will at the foot of the hill I will have a rest since I slow down to my average velocity - in this point I will start pedaling again.) or if I have rest by the way down the hill and start pedal again at the foot?
Is it preferable to pedal downhill?
bicycles.stackexchange.com
<racing-strategy>
bicycles.stackexchange.com/questions/24372
bicycles.stackexchange.com/users/13552/Klasická prádelní šňůra
There are different opinions among cyclists about pedalling down hill. Some believe it is a waste of energy as it increases your speed little and it is better to have a rest and be ready to face the next climb.  There is no need to pedal downhill on fun or fitness rides. Others see pedalling downhill as fun and enjoy reaching the maximum speed possible.  Moreover, if you are training for racing, it may be valuable. Due to wind resistance, it becomes exponentially more difficult to cycle faster at higher speeds. For that reason, on downhill sections it can be more effective to use an aerodynamic position to lower wind resistance and stay fresh for uphill sections. It can be fun to pedal downhill, but since it provides less advantage it can be helpful to rest before pedalling harder when you get to the bottom.
Due to wind resistance, it becomes exponentially more difficult to cycle faster at higher speeds. For that reason, on downhill sections it can be more effective to use an aerodynamic position to lower wind resistance and stay fresh for uphill sections. It can be fun to pedal downhill, but since it provides less advantage it can be helpful to rest before pedalling harder when you get to the bottom.