A math problem

I'd like to make a disc wheel cover for a conventional spoked wheel. Given that the surface of said
cover is the surface of a truncated cone, with the bottom diameter d1, the top diameter d2, and a
height of h1, what would be the outside diameter D1 and the inside diameter D2 if one cut the cone
surface and flattened into a plane? One ends up with a 'C' shape.

Thanks for the help.

Ken Lehner

 

Ken Lehner wrote:

>I'd like to make a disc wheel cover for a conventional spoked wheel. Given that the surface of said
>cover is the surface of a truncated cone, with the bottom diameter d1, the top diameter d2, and a
>height of h1, what would be the outside diameter D1 and the inside diameter D2 if one cut the cone
>surface and flattened into a plane? One ends up with a 'C' shape.
>
>Thanks for the help.
>
>Ken Lehner
>
>
D1 = SQRT(d1^2 + 4*(h1*d1/(d1-d2))^2 )

D2 = d2*D1/d1

You can solve for the cone angle instead, but it is not necessary.

What are you using for disc material?

Dave Lehnen

 

>D1 = SQRT(d1^2 + 4*(h1*d1/(d1-d2))^2 )
>
>D2 = d2*D1/d1

l guess this is right but there is a way to draw it which would(l think) be much easier and less
likely to lead to a mistake you want to draw a cross section (or 1/2 of one anyway) if you are using
sheet steel for the covers you can draw it on there, the corners should be pretty square you are
drawing a right angle triangle with a "base" of d1/2 the from the "opposite" end mark out d2/2 the
draw a line square to the base and mark out h1 on it ok this is where l gave up and have drawn a pic
but l cant post its 11kbs here have emailed it to you,hope it helps and that you e-mail is valid
mine isn't

 

[email protected] (Ken Lehner) wrote in message
news:<[email protected]>...
> I'd like to make a disc wheel cover for a conventional spoked wheel. Given that the surface of
> said cover is the surface of a truncated cone, with the bottom diameter d1, the top diameter d2,
> and a height of h1, what would be the outside diameter D1 and the inside diameter D2 if one cut
> the cone surface and flattened into a plane? One ends up with a 'C' shape.
> ----------------------

well, it wont *quite* be a cone since the areas between the spokes will more closely aproximate
facets. I dont think its worth it trying to get it too close. You'll be better off using fabric a
little big, probably in segments, and trimming "in situ".

I have a friend who did this years ago with model airplane paper/dope technique, gluing and
stretching over the spokes; it worked pretty good except that he always had trouble with a cutout
for the valvestem. If he left access, it started a rip, and sealing it shut meant cutting and
resealing whenever he pumped the tire. BUT, he did end up with a light disk wheel for a while.
Pretty delicate though from what I remember.

I think there were some fabric deals on the market for a while, but probably were removed due to
liability issues when they ripped and tangled in spokes...

d

 

sheet steel?? lol sorry misunderstood what you where making but that drawing still stands

 

On 4 Feb 2003, dan baker wrote:

....
> I think there were some fabric deals on the market for a while, but probably were removed due to
> liability issues when they ripped and tangled in spokes...

Dan,

The brand I remember was called Uni-Disk, stretchy fabric attached to lightweight hoops that clipped
inside the rim. I never heard of any problems such as you describe and I know of many users on
hpv's, where disk covers are allowed in racing <www.ihpva.org>. I even remember mtb'ers using these
with the claim that it kept sticks out of the spokes (but I have no direct experience with mtb use).

Do you have any direct knowledge of any accidents or are you making this up? My guess is that the
product wasn't very profitable and they quit...

I still make vacuum formed plastic wheel covers for Alex Moulton bikes (17" tires). Other members of
the IHPVA have made wheel covers in many creative ways.

-- Doug Milliken

 

[email protected] (Ken Lehner) wrote in message
news:<[email protected]>...
> I'd like to make a disc wheel cover for a conventional spoked wheel. Given that the surface of
> said cover is the surface of a truncated cone, with the bottom diameter d1, the top diameter d2,
> and a height of h1, what would be the outside diameter D1 and the inside diameter D2 if one cut
> the cone surface and flattened into a plane? One ends up with a 'C' shape.
>
> Thanks for the help.
>
> Ken Lehner

There's detailed instructions for three methods,plus a link to a fourth, at
http://www.wisil.recumbents.com/wisil/wheeldisk/wheeldisk.htm

Jeff

 

dan baker wrote:
>
> I think there were some fabric deals on the market for a while, but probably were removed due to
> liability issues when they ripped and tangled in spokes...
>

It may of been because the UCI would not allow any aerodynamic 'faring' on the bicycle. Disk wheels
had to be structural, not just a cover.

The rule might still be in place. I'm sure it would be lighter to cover a spoked wheel than build a
solid one.

--
Andy Morris

AndyAtJinkasDotFreeserve.Co.UK

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