Wind affect on going uphill and downhill question

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PK99

Legendary Member
Location
SW19
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.

No I'm not.

I'm pointing out that KV^2 a power function and K^V is an exponential function

Air resistance does not rise exponentially with velocity it rises with the square of velocity - a power function

Dictionary:

power-function
Noun mathematics)
a function where the independent variable is raised to some real number power.

exponential function
noun MATHEMATICS
a function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
 

Ajax Bay

Guru
Location
East Devon
When descending . . . the power released by gravity
Run that by me, please (kgm^2s^-3)?
 
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Alan O

Über Member
Location
Liverpool
Just an observation of something that's pretty common but which still surprises me - the ability of people to believe things that they know are true because an expert told them so, despite being surrounded by observational evidence to the contrary.

The falling objects thing is obviously the example here. Consider a) a leaf fluttering slowly to the ground and b) dropping something heavy on your foot. Who hasn't observed both of those things? Yet there are people who are very familiar with both phenomena, but who still insist that everyday objects all fall to ground with the same acceleration - because a school teacher once told them about an Italian dude throwing pizzas off a tower (or something).

As for Galileo and the tower of Pisa, he was essentially trying to disprove the Aristotelian view that acceleration in freefall is proportional to mass (and he never suggested that in real life objects fall at the same rate through air - I expect he'd seen leaves falling and had dropped things on his foot too). And he almost certainly never dropped anything off the tower - it was just a thought experiment based on considering how two objects would fall if they were connected by a piece of string. (see Wikipedia)

As another example, people repeated and believed Aristotle's apparent assertion that flies have four legs, when it was almost painfully easy to just look at one and see. (The claim that Aristotle said so may well have been a misunderstanding of what he meant, but it didn't stop people believing it without checking it.)

And didn't someone once prove that a moving bicycle can't fall over? I don't know about you, but I'm going to discard the wealth of personal evidence I have to the contrary, and start every ride with that assumption :whistle:
 

Ming the Merciless

There is no mercy
Photo Winner
Location
Inside my skull
No I'm not.

I'm pointing out that KV^2 a power function and K^V is an exponential function

Air resistance does not rise exponentially with velocity it rises with the square of velocity - a power function

Dictionary:

power-function
Noun mathematics)
a function where the independent variable is raised to some real number power.

exponential function
noun MATHEMATICS
a function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Then not sure whom you are responding to we we were referring the Physics definition of power, you know, that one that has an SI unit of Watts, force SI unit Newtons
 

PK99

Legendary Member
Location
SW19
2
Then not sure whom you are responding to we we were referring the Physics definition of power, you know, that one that has an SI unit of Watts, force SI unit Newtons

I was responding to you:

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

y=x^2 is a NOT and exponential function

Let me refer you again to the dictionary definition:

exponential function, noun,

a function whose value is a constant raised to the power of the argument, especially the function where the constant is e


A power function is a function of the form, f(x) = a.x^p,



It should be obvious that Velocity appears in the wind resistance equations as a power function and that your statement
Y = x^2 is an exponential function is simply wrong.

I think where you are getting confused is that in Y=x^2, 2 is the exponent, but the function Y=x^2 is a power function not an exponential function.

air_resistance_formula_1.png



Have a look here for futher guidance:

http://wmueller.com/precalculus/families/1_41.html

Powere functions f(x) = a x^ b

It is easy to confuse power functions with exponential functions. Both have a basic form that is given by two parameters. Both forms look very similar. In exponential functions, a fixed base is raised to a variable exponent. In power functions, however, a variable base is raised to a fixed exponent.

The parameter a serves as a simple scaling factor, moving the values of xb up or down as a increases or decreases, respectively

The parameter b , called either the exponent or the power, determines the function's rates of growth or decay. Depending on whether it is positive or negative, a whole number or a fraction, b will also determine the function's overall shape and behavior.
 
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swansonj

Guru
Don't you think, as evidenced in this thread, that the popular meaning of exponential is diverging and possibly has irrevocably diverged from the scientific one, and in popular usage exponential now just means anything that gets bigger more rapidly as it goes on?
 

PK99

Legendary Member
Location
SW19
Don't you think, as evidenced in this thread, that the popular meaning of exponential is diverging and possibly has irrevocably diverged from the scientific one, and in popular usage exponential now just means anything that gets bigger more rapidly as it goes on?

i certainly think that mathematical/scientific illiteracy has been amply demonstrated.
 

PK99

Legendary Member
Location
SW19
[QUOTE 5259968, member: 9609"]going back to my post where I said "the effect of the wind is exponential" How should I have worded it ? what word should I have used in stead of exponential .


And I'm still not quite getting what an exponential function is.
y^x would be exponential cause x is a variable
but once x is given the value of 2 or 3 or 9 it stops being exponential ?[/QUOTE]

"air resistance increases rapidly with velocity " would be correct. This implies a non linear relationship without being speific about the form.

A power function is of the form :
Variable to some power.
In this case, Velocity squared. ie v^2

An exponential function is of the form: a constant to a variable power.
In this case K to the power of velocity. ie k^V.

Does that make sense?
 
It's like maths before my third cup of coffee.... :scratch:

I have had a couple of entertainingly silly wind-related hilly moments. Once went for a ride out from Darlo to assorted tall-sounding places with a few mates led by @Skuhravy quite early in the year and, as they often do, our glorious leader planned a route with the wind at our backs for the second half. I had the most disconcerting experience of having to apply the brakes while going uphill to avoid running into his (fixed) rear wheel, while watching water flow uphill. Just a little bit of tailwind there that day.

I also once had to pedal downhill on most of that swoopy road between Redmire and Hawes, through Carperby and Askrigg, because of the ferocious headwind.
 

PK99

Legendary Member
Location
SW19
[QUOTE 5260343, member: 10119"]It's like maths before my third cup of coffee.... :scratch:

I have had a couple of entertainingly silly wind-related hilly moments. Once went for a ride out from Darlo to assorted tall-sounding places with a few mates led by @Skuhravy quite early in the year and, as they often do, our glorious leader planned a route with the wind at our backs for the second half. I had the most disconcerting experience of having to apply the brakes while going uphill to avoid running into his (fixed) rear wheel, while watching water flow uphill. Just a little bit of tailwind there that day.

I also once had to pedal downhill on most of that swoopy road between Redmire and Hawes, through Carperby and Askrigg, because of the ferocious headwind.[/QUOTE]

I came down Ventoux into a headwind a couple of years ago, maxing out at around 15mph without using the brakes
 

gavroche

Getting old but not past it
Location
North Wales
After reading some of those exposes, I have come to the conclusion that there are some clever people on this forum, so , as it all goes over my head, I'm out.
 
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