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This is a hypothetical question but I'm curious. Assuming an endless, freshly paved road with no turns, what would be my maximum speed?

EDIT My question is too general so to help I'm adding some extra assumptions:

  • 19 degree slope like Baldwin St.
  • Tuck is hands on drops, back horizontal as described in this study
  • Still air conditions (no head/tail/crosswinds) winds
  • No special suit, just normal warm weather road kit
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  • en.wikipedia.org/wiki/List_of_cycling_records
    – mootmoot
    Jul 28, 2017 at 14:22
  • Even at a fast everyday downhill riding speed of +40mph the difference between hoods and drops is dramatic -- every little bit of drag counts. So there is no tucked vs. not tucked; it's a continuum. Steepness makes a big difference -- how steep a hill can your hypothetical bike descend? This will very with the height of the centre of gravity -- more tucked will mean a steeper slope before your C of G is over the front axle as well as with the wheelbase. Are you considering pedalling or not?
    – Chris H
    Jul 28, 2017 at 14:42
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    I once broke 60 on a downhill. But I very quickly reined it in after I hit that mark, since going that fast is scary. In such a situation sitting upright vs riding on the drops probably cuts top speed 15-20 mph.
    – Daniel R Hicks
    Jul 28, 2017 at 22:04
  • +1 for Baldwin Street in Dunedin. That is one damn scary road.
    – Criggie ♦
    Jul 28, 2017 at 23:04
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    -1 for substantially changing a question with an answer.
    – paparazzo
    Jul 29, 2017 at 1:50

4 Answers 4

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The question has been changed since this answer was posted.

On an 85° grade you would approach terminal velocity for a sky diver of about 120 mph.

It does not need to be endless. You approach terminal velocity pretty quickly.

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    I think we have to account for elevation. Assuming the track is endless we can assume you are starting off at 100,000 feet where the atmosphere is thinner which will increase your terminal velocity.
    – Kibbee
    Jul 28, 2017 at 13:21
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    @Kibbee Gravity would be less also. Not going down that road with you.
    – paparazzo
    Jul 28, 2017 at 13:32
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    At 100,000 feet we still have about 99% of the gravity on sea level. Less atmospheric drag will be the dominating effect. Unless of corse we start much further outside, say near the moon.
    – linac
    Jul 28, 2017 at 13:52
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    Btw, a 90% grade would "only" be 42°. I don't think that's enough for the terminal velocity of a sky diver.
    – linac
    Jul 28, 2017 at 14:14
  • Skydivers typically adopt a very un-aerodynamic position: I'd expect a tucked cyclist to have a rather higher terminal velocity. According to Wikipedia, diving head-down (as if diving into a pool from a diving board) will get you to over 300mph, and Felix Baumgartner got to over 800mph on his high-altitude record jump.
    – David Richerby
    Jul 28, 2017 at 23:27
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Terminal velocity is reached when the force on the rider due to gravitation acceleration equals the force from aerodynamic drag on the rider and bicycle plus rolling resistance of the bicycle.

In the calculation below I will assume rolling resistance of the bicycle is much less than the air drag and will omit it. I may update this later. I will use typical values for gravity, air density etc at sea level on Planet Earth.

Gravitational force on the rider and bike F = m × g × sin(ϕ)

  • m is mass of rider and bike 80kg for rider 10kg for bike is 90kg
  • g is gravitational acceleration 9.81 m/s²
  • ϕ is the slope in radians, 19° is 0.33 radians

That yields a force of approx. 287.4 Newtons

Aerodynamic drag force is CdA × ρ × v² / 2

  • CdA is drag coefficient × frontal area, I'll use a figure of 0.275 from the page linked to by the OP.
  • ρ is air density 1.225 kg/m²
  • v is velocity.

Terminal velocity is therefore √ ( 2 F / ( CdA × ρ ) ) which yields 41.3 m/s or about 149 km/h, 92.5 mph.

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  • That seems high to me.
    – paparazzo
    Jul 31, 2017 at 15:17
  • @Paparazzi, yeah I have to admit it seems high to me too. I'm looking for data to back it up or prove it's in the right ballpark.
    – Argenti Apparatus
    Jul 31, 2017 at 15:50
  • @Paparazzi ... although the road referenced by the OP is crazy steep. Interestingly, if I plug 45° (the max slope of a double diamond ski run, according to Wikipedia) into my calculation, I get about 220km/h, which is comparable with the speeds in the table L.Dutch provided
    – Argenti Apparatus
    Jul 31, 2017 at 16:14
  • Might be good. I saw a racer stat of 85 mph on 10°. But 160 mph for 90° still seems high but terminal velocity I quoted is based on spread out.
    – paparazzo
    Jul 31, 2017 at 16:39
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    I agree. I still don't like the OP changed a question that much rather than accept my answer but no big deal.
    – paparazzo
    Jul 31, 2017 at 18:28
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Claudio Chiappucci reported that during the World Championship in Colombia in 1995 he had reached 90 kmh.

Then you can also visit this page, where you can find this table

enter image description here

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    90 kph on a road bike is fairly slow. It is not uncommon to hit 100 kph+ on a descent in a race. I used to hit 85 kph almost daily on a commute.
    – Rider_X
    Jul 31, 2017 at 2:20
  • @Rider_X you must ride like a madman
    – Byron Whitlock
    Jul 31, 2017 at 4:33
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I know nothing about the theory. But the world record for gravity bike is, according to Guinness, 103km/h. (http://www.guinnessworldrecords.com/world-records/71665-fastest-gravity-speed-bike)

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