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Re: math expression : any wizzkids out there ?

Theo
I've been searching the internet for answers and I found that it's not the sinus I need but the tangens. With sinus the diagonal distance is known but the computer of the treadmill only measures the horizontal distance walked. Therefore the formula uses the tangens.


I believe you're mistaken, Theo.

The only fixed distance the treadmill is aware of is the length of the moving belt, because you are walking along its length. By walking along it, the machine calculates the distance you have walked along the belt. As the belt is tilted upwards, it becomes the hypotenuse of the triangle. So the height gained is in fact a function of the sine of the angle the ramp is elevated.



Re: math expression : any wizzkids out there ?

What Mr Sloman said and also Patrick & I said Theo.

The treadmill is at an angle.
You are effectively walking along the hypotenuse.
So the formula is

height = distance x sin(angle of elevation)

See the diagram above

OK, it's all and estimation but pretty good one.

Al was an engineer and I taught maths (about 25 years ago I admit)


The confusion is probably because there is NO elevation in Holland

Re: math expression : any wizzkids out there ?

...and that is why I got no further than O' Level (and a B in that was a surprise...)

Re: math expression : any wizzkids out there ?

But, but, but......if I walk 1000m on a treadmill at an angle of 45 dgrs using the sinus gives an outcome of 707m of ascent while using the tangent gives an outcome of 1000m of ascent.
An angle of 45 dgrs means it has a straight corner (90 degr), therefore the horizontal is 1000m as well as the vertical. Ergo I have ascended 1000m.

As Johan Cruyff would say : you'll see it when you get it.

Re: math expression : any wizzkids out there ?

I suppose this only proves the old adage of "You can lead a horse to water..."

Theo: Walking 1000m on your treadmill inclined at 45degrees simply means that you have covered a horizontal distance of 1000 x cos 45% = 707m. And in those 707 horizontal metres you have climbed 707 vertical metres.


"As Johan Cruyff would say : you'll see it when you get it."

Re: math expression : any wizzkids out there ?

The angle of the treadmill doesn't really matter. The belt of the treadmill is approximately 4m all the way round. After 250 rounds you've walked 1000m, whether the treadmill is angled at 45 dgrs or even 225 dgrs (which would lead to a descent).
A rectangular triangle has 2 equal sides, whatever way it's positioned. The computer of the treadmill doesn't know whether it's upside down or not).
If I walk 1000m from A to B on the map and the track has a constant angle of 45 dgrs. and I end up on a mountain 1000m high, how much have I ascended ?

Re: math expression : any wizzkids out there ?

If you won't listen to mathematical reasoning, try this:

If it was possible to angle your treadmill 90 degrees, ie vertically, and it is possible for Fred the Mathematical Fly to walk along it for 1000m, how far do you think Fred will have walked in a horizontal direction, Theo?

The answer is he won't have walked in a horizontal direction at all. He will have only scaled 1000m

1000 x Cos90 = Zero.
1000 x Sin90 = 1000.

Re: math expression : any wizzkids out there ?

Als ik zou willen dat je het begreep, legde ik het wel beter uit. (A Cruijffiaan . . . )

Re: math expression : any wizzkids out there ?

Alan is completely right. This website introducing elementary trigonometry explains.

Re: math expression : any wizzkids out there ?

Ian Sommerville
Alan is completely right. This website introducing elementary trigonometry explains.


That's what I said Ian.

I studied maths, and taught it for 13 years.
I must have destroyed the maths careers of so many children.
Oh, apart from the ones who ended up with a 1st in maths at Uni.
And they did that without trigonometry

Theo sir.
Listen to professor Sloman.
Actually listen to Ian. he's a real professor!

Trigonometry

Re: math expression : any wizzkids out there ?

To follow that last one up Theo.
Pythagorous.

Slope ^ 2 = Horizontal Distance ^ 2 + Height ^ 2

So if the treadmill is at 45 deg.

And you walk 1000m at 45 Deg.

Horizontal distance = 707m and Height = 707m

Check it out

Remember 707 is a rounded answer
Calculated using the Sine.

707^2 + 707^2
= 499849 + 499849
= 999698

And Square Root of 999698
=999.9
Or
1000 to the nearest whole number.

Confused?

Re: math expression : any wizzkids out there ?

I figured it out yesterday while taking a shower. What really helped me was Humpries comment (in Dutch) : if I wanted you to understand it I would have explained it better.
So what was missing in Alan's and Andrews explanation ? I gathered if you walk horizontally (on the map/a treadmill) for 1km at an angle of 45 dgrs. you end up 1km higher. The missing link was the fact that with 250 rounds of 4m belt of the treadmill you have to walk further to cover 1km horizontally (a2+b2=c2). It's a bit like having a computerproblem and the nerd shows you how to solve it. 20 seconds and 20 clicks later you haven't got a clou what he has done.

Thanks Humph : je gaat het pas zien als je het snapt.

So sine it will be (****, more walking to reach the virtual summit).

Re: math expression : any wizzkids out there ?

So, Theo, what part of

"Theo: Walking 1000m on your treadmill inclined at 45degrees simply means that you have covered a horizontal distance of 1000 x cos 45% = 707m. And in those 707 horizontal metres you have climbed 707 vertical metres."

did you not understand?

Taking a swipe at those trying to help you, and likening them to computer nerds is not big or clever, Sir.



Re: math expression : any wizzkids out there ?

Well, you did at least work it out Theo.
But..
The only missing thing in the answers were the fact they weren't in Dutch, and your ability to understand.
You can't get much simpler than a great big diagram explaining all the dimensions.
I must have been a dreadful maths teacher. And I never knew.

Re: math expression : any wizzkids out there ?

I didn't compare you or Andrew with computernerds, I compared the situation where people who are specialists try to explain or show how things work to people who don't understand one bit like me. I'm sorry if I gave you the wrong impression.

Re: math expression : any wizzkids out there ?

Aye Theo, it's all very confusing. I skipped school on the day they explained the hard sums. I blame Imperial measurements, avoirdupois and troy weights, poles and perches, chains and leagues, Fahrenheit and such like. The next thing is they will try to impose Napoleonic decimal systems on us. It will never catch on.

Re: math expression : any wizzkids out there ?

Here's the calculation for angles up to 20 degrees. For every horizontal km run, this is the height gain. So, if you set the treadmill at 6 degrees and run 1 km, you will be 105 metres higher than when you started.

0 0
1 17
2 35
3 52
4 70
5 87
6 105
7 123
8 141
9 158
10 176
11 194
12 213
13 231
14 249
15 268
16 287
17 306
18 325
19 344
20 364

Re: math expression : any wizzkids out there ?

Not a single challenger has given the right answer to Theo's joke!

Theo, no matter how long you walk on your treadmill, no matter at what angle you fix it, the result is that you have walked 0 kilometres and 0 metres height gained.
Go out and have a real walk in a real environment!

Even in our own Netherlands there are enough little hills to get some physical exercise in walking uphill. For instance, go to Nijmegen and walk the old 20km N70 route. Though the hills are only 100m high, When you have done the route you will have gained more than 500m height.

Cheers, BART

Re: math expression : any wizzkids out there ?


Spot on, Bart. That's the trouble with abstract thinking!

Re: math expression : any wizzkids out there ?

Hi Bart,
my brother lives at the top of an appartmentbuilding and I used to go up and down the staircase will full backpack. Up was tough but going down always came to soon for proper stamina.
1,5k/20%/10kg will let me sweat a lot without driving for 80 min to Nijmegen.