radius-formula

[dEFcHILL]

hello,

do u have a formula, how to calcualte the radius of a ski.

for example: length=185m sidecut=(119-87-111)mm--->radius=22,4m


thx

[littleKam]

You should be able to calculate the radius given the waist, tip, and tail width dimensions using simple geometric formulas. i don't have the exact formulas right now but i think this is how i found the radius:

1. find the formula of the straight line running running from the tip and tail widths (called the chord length).
2. find the distance of this straight line to the waist of the ski (called the arc height).
3. using the chord length and arc height you can find the radius of the ski.

[Guest]

hello,

1st, thank u..

i tried it to calculate with polar-koordinates. i put the sidecut of the ski in a polar coordinate system. with the most narrow part (middle of the ski) on the x-line and , i put the profile of the ski together with the out side line of a cyrcle. [ pollar-coordinate: (cos[alpha])=x ; r(sin[alpha])=y ]
my calculations should be right, but on comparition with already existing skis and there sidecut+radius, i became different results.


but anyway-->here is a nice site, where iz explained really good--> http://www.math.utah.edu/~eyre/rsbfaq/physics.html

[G]

Here is a quick and fairly accurate way to get the radius from the ski dimensions:

L = total length of ski in cm
TP = tip width in mm
W = waist width in mm
TL = tail width in mm

First we have to make an assumption as to how much of the ski's length is part of the actual radius. I have found that 85% is reasonable, so we can determine (but if you know the actual chord length use it instead):

CL = chord length = .85 * L

Next we approximate the distance perpindicular to the chord to the radius and convert it into cm:

D = ((TP + TL)/2 - W)/20

Finally we apply an approximation to the radius and convert to meters:

R = CL*CL / (D*800)

Using your dimensions we have:

TP = 119 W = 87 TL = 111 L = 185

CL = .85 * 185 = 157.25
D = ((119 + 111)/2 - 87)/20
= (115 - 87)/20
= 28/20 = 1.4
R = 157.25 * 157.25 / (1.4 * 800)
= 24,727.56/1120
= 22.1 meters

which is fairly close to the 22.4 specified. You would need the exact chord length to get this answer closer and replace that with the estimated 157.25 number

Working in reverse you can calculate the chord length from the data you provided, and it would be 158.35 cm based on the 22.4 m radius. So you can see that the estimate of 157.25 is close.

[Mutombo]

Hi! I´m new here and i´ve to say you have a great web, a lot info, I´ll try to do my skis (buying skis age has now ended haha).
I have a doubt I hope you´ll be able to answer me. I don´t understand too much where those formulas come from, my question is if the carvin radius is de circle that goes through three points: the contact point in the tip and tail and the one in the most narrow part of the waist.
Thx 4 all!!

[G]

Yes, you are correct. The formula assumes that 3 points are used to define the radius, and the 3 points are exactly what you described.

[endre]

here's the exel formula for calculating radius.

radius=length^2/((tip+tail-2*waist)*2)/10


be very accurate when measuring the lengths between the measuring points of tip and tail. Actually it doesn't matter if you measure just a 50cm. section of the midski or the whole length (as long as the edge is truly radial). It is very important that "length" is the true length between the measured "tip" and "waist" (which doesn't have to be the the widest parts of the ski)

actually even the ski manufacturers sometimes miss this point. new skis often have a wider tip than the width at the contact point (which is the end of the chord length). Out of old habit they put the ski width, (widest parts of the ski) and the chord length into this formula, this generates a too short radius.

f. ex the 2007 big daddy claims to have a 41m. R, I found a radius of 59m. (this is extreme though, mostly the numbers are correct)

[Mutombo]

Thx for ur answers, I think I´m gonna use AutoCad to draw the circle and then check the radius.
I´ll be here to do more questions to you hehe. We are asking for prices for the materials and I hope we start making our skis very soon, I´ll tell you.
Thx!!

[Buuk]

To be more exact, the method of calculating the radius of an arc defined by three points is given by:
r = (4·length^2 + (tip + tail - 2·waist)^2)/(8·(tip + tail - 2·waist)) ...
according to Pythagoras r^2=x^2+y^2

[zachjowi]

is there any CAD drawings people have made of their skis?

[PTTR]

old tread but this link makes it all so easy:

http://www.mathopenref.com/arcradius.html

[SHIF]

is there any CAD drawings people have made of their skis?

http://www.skibuilders.com/phpBB2/viewtopic.php?t=3135

-S