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Coasting down hill

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Road Cycling “It is by riding a bicycle that you learn the contours of a country best, since you have to sweat up the hills and coast down them. Thus you remember them as they actually are, while in a motor car only a high hill impresses you, and you have no such accurate remembrance of country you have driven through as you gain by riding a bicycle.” -- Ernest Hemingway

Coasting down hill

Old 05-27-22, 05:44 PM
  #76  
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Originally Posted by Bah Humbug View Post
Was this thread ever serious?
The part that I posted about going Superman style is dead serious.
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Old 05-27-22, 05:44 PM
  #77  
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P ∝ v3

It is cubic. It is not squared, exponential or quadratic.

Double the speed from 20 mph to 40 mph requires 8 times the power to overcome the resistance of air.
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Old 05-27-22, 05:46 PM
  #78  
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Originally Posted by GhostRider62 View Post
P ∝ v3

It is cubic. It is not squared, exponential or quadratic.

Double the speed from 20 mph to 40 mph requires 8 times the power to overcome the resistance of air.
in my case doubling the speed to 40mph requires one big f’in hill.
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Old 05-27-22, 05:48 PM
  #79  
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Originally Posted by GhostRider62 View Post
P ∝ v3

It is cubic. It is not squared, exponential or quadratic.

Double the speed from 20 mph to 40 mph requires 8 times the power to overcome the resistance of air.
Aerodynamic drag is quadratic. Power required to overcome aerodynamic drag is cubic.
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Old 05-27-22, 06:11 PM
  #80  
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Originally Posted by tomato coupe View Post
Aerodynamic drag is quadratic. Power required to overcome aerodynamic drag is cubic.
I am not sure what you are saying. Do you?

I was stating the power and speed relationship to overcome the resistance of air. It is cubic.

Drag is the force to overcome air resistance and it is quadratic. Power required is force times velocity and is therefore cubic.

We only care about speed and power. The only relationship that matters is double your speed requires 2 x 2 x 2 in power or a factor of 8.

WRT to the topic at hand, there is a speed where it makes much more sense to tuck and reduce CdA than to keep pedaling. It varies. I stop for sure at 38 mph.
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Old 05-27-22, 06:47 PM
  #81  
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Originally Posted by GhostRider62 View Post
I am not sure what you are saying. Do you?

I was stating the power and speed relationship to overcome the resistance of air. It is cubic.

Drag is the force to overcome air resistance and it is quadratic. Power required is force times velocity and is therefore cubic.

We only care about speed and power. The only relationship that matters is double your speed requires 2 x 2 x 2 in power or a factor of 8.

WRT to the topic at hand, there is a speed where it makes much more sense to tuck and reduce CdA than to keep pedaling. It varies. I stop for sure at 38 mph.
The original statement was "Air resistance [drag] increases exponentially with speed." That is incorrect -- drag is a quadratic function of speed. You introduced P, and made a statement that "It is cubic. It is not squared, exponential or quadratic." I was simply clarifying that aerodynamic drag is a quadratic function of speed, and the power required to overcome drag is a cubic function of speed, as some people may not have realized that you had changed the topic from drag to power. I stated exactly what you repeated in your 3rd paragraph.

Last edited by tomato coupe; 05-27-22 at 06:57 PM.
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Old 05-27-22, 07:33 PM
  #82  
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Originally Posted by tomato coupe View Post
That's fine and dandy, but it still means a 100kg cyclist would have to spin at 220 RPM to reach 200 W, which barely touches the "hundreds of watts" stated by the OP.
No, it increases faster than a linear function. Based on the published data points at 50, 70, 90 and 110 rpm, it increases roughly as a cubic function. So it will reach 2W/kg at about 135 rpm.

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Old 05-27-22, 07:42 PM
  #83  
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Originally Posted by ofajen View Post
No, it increases faster than a linear function. Based on the published data points at 50, 70, 90 and 110 rpm, it increases roughly as a cubic function. So it will reach 2W/kg at about 135 rpm.
Okay, so the 100 kg cyclist needs to get up in the 160-175 RPM range to burn hundreds of watts. I don't think the OP is soft pedaling at that cadence.
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Old 05-27-22, 07:49 PM
  #84  
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Originally Posted by tomato coupe View Post
Okay, so the 100 kg cyclist needs to get up in the 160-175 RPM range to burn hundreds of watts. I don't think the OP is soft pedaling at that cadence.
That would be about 325-425W, so, yeah that would be a lot.

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Old 05-27-22, 09:37 PM
  #85  
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Originally Posted by tomato coupe View Post
Okay, so the 100 kg cyclist needs to get up in the 160-175 RPM range to burn hundreds of watts. I don't think the OP is soft pedaling at that cadence.
try holding a high cadence, it gets ridiculously inefficient after a certain point. i attempt to soft pedal at 150+ rpm and it destroys me
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Old 05-27-22, 09:43 PM
  #86  
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Originally Posted by LarrySellerz View Post
try holding a high cadence, it gets ridiculously inefficient after a certain point. i attempt to soft pedal at 150+ rpm and it destroys me
Forgive my lack of trust, but I doubt you spend any time at 150+ RPM.
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Old 05-27-22, 09:46 PM
  #87  
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I don't pedal when going down hill and all my rides are up and down. So really my 10 mile rides are only 5 and my 15 only 7... Go Figure...
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No matter where your at... There you are... Δf:=f(1/2)-f(-1/2)
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Old 05-27-22, 09:57 PM
  #88  
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Originally Posted by tomato coupe View Post
Forgive my lack of trust, but I doubt you spend any time at 150+ RPM.
I attempt to follow fast groups on a 42x18 ss, its kind of silly but its increased my max cadence a ton. 150 is only 27.5 mph. I struggle a lot at that speed but I try
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Old 05-28-22, 07:39 AM
  #89  
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Totally anecdotal, and I am an old orangutan on an old mtb, but I experimented with wind resistance, highest cadence, and max speed on my steepest hill. Whether I pedal to 25mph and "tuck", or pedal like mad all the way down, I still top out at 35-36 mph. Hundreds of trials. Again, totally unscientific, and no superman! 40x11 chain ring/sprocket.
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Old 05-28-22, 08:06 AM
  #90  
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Originally Posted by tomato coupe View Post
The original statement was "Air resistance [drag] increases exponentially with speed." That is incorrect -- drag is a quadratic function of speed. You introduced P, and made a statement that "It is cubic. It is not squared, exponential or quadratic." I was simply clarifying that aerodynamic drag is a quadratic function of speed, and the power required to overcome drag is a cubic function of speed, as some people may not have realized that you had changed the topic from drag to power. I stated exactly what you repeated in your 3rd paragraph.

I think it is less confusing to simply state that drag is proportional to v squared and Power is proportional to v cubed.

To me (maybe being UK educated in maths?) a quadratic function implies a quadratic equation of the form ax^2 + bx + c = 0 which the drag equation isn't.
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Old 05-28-22, 08:23 AM
  #91  
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Originally Posted by PeteHski View Post
I think it is less confusing to simply state that drag is proportional to v squared and Power is proportional to v cubed.
Nothing wrong with that if it is your preference.

To me (maybe being UK educated in maths?) a quadratic function implies a quadratic equation of the form ax^2 + bx + c = 0 which the drag equation isn't.
Quadratic means the highest power is two (i.e. squared). It doesn't imply the existence of the other terms in the quadratic equation.
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Old 05-28-22, 12:19 PM
  #92  
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Originally Posted by bampilot06 View Post
Airport Crew room is about the same experience, so, yes I did.
Legitimately counting time spent in the crew room as rest is tricky, even when bunks and such are provided. So unless you know what the FAA will say, I hope you counted that as duty time.
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Old 05-28-22, 12:44 PM
  #93  
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Originally Posted by Iride01 View Post
Legitimately counting time spent in the crew room as rest is tricky, even when bunks and such are provided. So unless you know what the FAA will say, I hope you counted that as duty time.

I only sleep in the crew room when I am trying to get home. If I have to work I get a hotel. I have no interest in making the news.
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Old 05-28-22, 12:45 PM
  #94  
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Originally Posted by Broctoon View Post
On anything more than a moderately steep descent, your pedaling effort will be wasted. This is because aerodynamic drag (and therefore power required to increase speed) goes up by the square of your speed increase.

Going up a hill, obviously you must pedal to keep moving. It's okay, because at speeds below 10 or 15 mph, air drag is by far the smallest component of the total formula you have to overcome to maintain or increase speed. In other words, your effort is not wasted, because increasing power by 20% will bring an increase in speed of nearly 20%

On flat ground, pedaling is again required, obviously. At speeds of 15 to 20 or 22 mph, air drag starts to take over as the major component. Within this range, any increase in speed will require a progressively greater effort--actually, this is always the case, but in this range it becomes a significant factor.

When you're coasting downhill at 25, 30, 35 mph or higher, you might as well rest and enjoy the free propulsion from gravity (technically, withdrawing potential energy you put in the bank while climbing earlier on your route, or if your descent is at the beginning of the route, going in debt by using energy you haven't banked yet). To increase your speed, you'll have to exert a disproportionately greater effort. Spending any energy here does little to increase speed, therefore it's better saved for a time when it will make a bigger difference.
Exactly right. Haven't see anyone else explain this properly.
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Old 05-28-22, 03:09 PM
  #95  
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Originally Posted by tomato coupe View Post
Nothing wrong with that if it is your preference.


Quadratic means the highest power is two (i.e. squared). It doesn't imply the existence of the other terms in the quadratic equation.
Yeah I realise that now. It's just that over here we always use the term "squared" when talking about the relationship of one variable to another i.e. in this case Drag being proportional to v squared. But anyway, we are talking about exactly the same thing. No disagreement there, just different terminology.
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Old 05-28-22, 07:47 PM
  #96  
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Originally Posted by larrysellerz View Post
i dont really know what to think tbh
qft
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Old 05-28-22, 09:33 PM
  #97  
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I'm a Randonneur; I ride long distances and do so entirely by feel rather than with power or heart data. My sense is I benefit from going a little deep on climbs, but not too far. There's a strong tendency to go too hard, and pay the price later on the ride.

Early it's tempting to jump on a faster group, benefit from the draft, and bury myself to stay with them on the climbs. Following that strategy will leave me dropped, faced with hours of being passed one by one by riders who started more wisely. I avoid that trap as best i can. Too much effort on climbs hurts in the long run, not even offset by having drafting partners.

On the downhill side, clearly the speed benefit from pedaling downhill diminishes with grade; however, there are other reasons to pedal and other reasons to coast.

Spinning up after a long coast can be painful. Muscles and knees get stiff; maybe even inflammation starts ramping up. I'm not talking about little rollers, I'm talking long climbs and descents. Soft pedaling keeps things limber. OTOH, coasting provides the opportunity to unload weight off your saddle, put your body in another position for a while. At some point, comfortable is faster than the alternative. Nobody ever DNF'd from being comfortable.

Last edited by downtube42; 05-28-22 at 11:49 PM.
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Old 05-28-22, 09:46 PM
  #98  
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Originally Posted by PeteHski View Post
Yeah I realise that now. It's just that over here we always use the term "squared" when talking about the relationship of one variable to another i.e. in this case Drag being proportional to v squared. But anyway, we are talking about exactly the same thing. No disagreement there, just different terminology.
You aren’t wrong. * The other coefficients are just zero for the case.

https://en.wikipedia.org/wiki/Quadratic_equation

* it just doesn’t matter for this discussion.


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Old 05-28-22, 10:47 PM
  #99  
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Originally Posted by njkayaker View Post
You aren’t wrong. * The other coefficients are just zero for the case.

https://en.wikipedia.org/wiki/Quadratic_equation

* it just doesn’t matter for this discussion.
No, it doesn't matter for this discussion, but ... you're confusing the quadratic equation, which is an algebraic expression, with quadratic functions.
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Old 05-29-22, 03:30 AM
  #100  
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Originally Posted by genejockey View Post
I'm not sure how much more speed you can gain by pushing harder on the descents. Mostly, I spin up to 25 or so and then coast, on the straight ones. The technical ones, I'm braking WAY more than I'm pedaling. I think you'd lose more by going less hard up the hills than you'd gain pushing more on the descents. And, geez - you say you weigh 260. How much more speed do you need than what that gives you? You could probably get more speed by rebuilding your hubs with new grease and bearings.
its funny, im huge but due to a neck injury am not aerodynamic at all. At high speeds I struggle, smaller riders with a more aggressive position pull ahead. For instance going down Alpine, the fast groups are going over 30 mph and ive been dropped thinking I would just ride away from the field because I have an extra 100 lbs on the average rider. Aerodynamics are so huge at high speeds, I find that even though im 260 lbs I'm strongest on false flats and headwinds where power is king. I think the benefit of weight is overstated on descents unless the rider is flexible and aero.
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