Wind affect on going uphill and downhill question

[Ming the Merciless]

Were you cycling up Everest in the Jet Stream then crashed into a crevasse on the way down?

 

[Ming the Merciless]

[QUOTE 5258327, member: 9609"]yes you seem to be correct and may be I should of used the term quadratic ? (learn something everyday)
I still feel exponential is still quite a good description and would be more meaningful to most.?

anyway what is the relationship between wind and drag, I always thought it was squared but some reckon it is cubed, or are they just rough guides and is it just more complicated than such a simple formula. ?[/QUOTE]
Drag which is a force is proportional to the square of the velocity. Power is proportional to the cube of the velocity. Double the velocity and you get four times the drag to overcome, but need eight times the power.

 

[PK99]

Nothing stopping x being 2 or 3. Y = x^2 is an exponential function as is y=x^3. Y = x^4 etc.

@DaveReading is correct

The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.

In the case of air resistance,

Resistance F = KV^2 a power relationship

An exponential relationship would be of the form F =K^V

See:

http://www.softschools.com/formulas/physics/air_resistance_formula/85/

 

[DaveReading]

Nothing stopping x being 2 or 3.

Well then all you've done is ignore the convention that x in an equation is the independent variable, and instead make it a constant. And then assume that a (in my "y = a to the power of x" example) is the variable and not a constant.

You got me there.

 

[Ming the Merciless]

@DaveReading is correct

The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.

View attachment 411307

In the case of air resistance,

Resistance F = KV^2 a power relationship

An exponential relationship would be of the form F =K^V

See:

http://www.softschools.com/formulas/physics/air_resistance_formula/85/

You are mixing the meaning of power and force in Physics with the different meaning in mathematics. But anyway none of this is helping Accy answer his question. The true answer is probably he beasted himself uphill and was then too tired to pedal downhill.

 

[swansonj]

You are mixing the meaning of power and force in Physics with the different meaning in mathematics. But anyway none of this is helping Accy answer his question. The true answer is probably he beasted himself uphill and was then too tired to pedal downhill.

In a different thread, @srw and I have just been confused with each other. One of the differences is that he is a mathematician and I am a physicist. I'm going to take a punt that neither of us knew that power and force have different meanings in maths and physics (but that we both knew that exponential is used colloquially in a way that differs from the scientific meaning).

 

[DaveReading]

It's all becoming a bit of a drag.

 

[MontyVeda]

Particularly when they’re made up...

they're my favourite sort of facts.

 

[swansonj]

When climbing, your power is mostly going into overcoming gravity, not wind resistance. So however much wi d resistance changes because of a headwind or tail wind, it won't make a lot of difference.

When descending, at higher speed, the power released by gravity, augmented by whatever pedalling you do, is almost entirely going in to overcoming wind resistance. So changes in wind direction and speed should make a much bigger difference to your speed.

BTW, the power used to overcome wind isn't as simple as force=square of speed so power = force times speed = cube of speed. The force is the square of the relative speed of you and the wind. The speed you multiply by is your ground speed. Only in zero wind is power strictly proportional to speed cubed.

 

[srw]

In a different thread, @srw and I have just been confused with each other. One of the differences is that he is a mathematician and I am a physicist. I'm going to take a punt that neither of us knew that power and force have different meanings in maths and physics (but that we both knew that exponential is used colloquially in a way that differs from the scientific meaning).

I don't think they do - because in maths they're only used in mechanics, which is basically physics by another name.

And I also don't think that "exponential" is usually used colloquially in the way I've seen it used in this thread - which I'd describe using the extremely technical adjective "wrong". Of course the philosopher in me wants to remember that words mean what people use them to mean, so if the word is becoming used to refer to polynomials then it is changing its meaning. Which is going to be a bit of a bugger, because its a commonplace that exponentials grow quicker than any polynomial.

And the linguistic pedant in me is squishing the philosopher to observe that the word "affect" in the thread title should be "effect". Unless we really are talking an emotional impact.

 

[DCBassman]

+1 about 'affect'...

 

[Milzy]

I don't know. I'm waiting for a CC scientist to come on and explain it to me. I think it'll take someone with at least a degree in Physics,or something like that. Mind you,the other week i said that going downhill on a carbon fibre bike was harder than on a steel one, as with it being lighter it won't descend/fall as fast. Someone down my local pub after i'd made the comment told me that all objects descend/fall at the same speed no matter their weight or shape. I still can't get my head round or accept that one.

If you create a room with zero gravity I’m pretty sure if a feather and a brick were dropped at exactly the same time, they’d both touch the bottom at exactly the same time. I haven’t done physics for over 25 years mind.

 

[DCBassman]

If you create a room with a vacuum I’m pretty sure if a feather and a brick were dropped at exactly the same time, they’d both touch the bottom at exactly the same time. I haven’t done physics for over 25 years mind.

Fixed zero-g for vacuum.
Brian Cox has done this at NASA. It was really weird to watch...

 

[Milzy]

Fixed zero-g for vacuum.
Brian Cox has done this at NASA. It was really weird to watch...

Almost put that too. Thanks.

 

[Serge]

The simple test is get a small 1kg metal sphere and a 1kg Piece of cardboard with a huge surface area. Drop both from 100m up and they will not hit the ground at the same time.

An even simpler test is to get two identical umbrellas, open just one and drop them both. I very much doubt they'd hit the ground at the same time.