Trigonometry: please check my working

OK, so I've got a wheel with a brake disc that is held on with three
bolts, arranged equally round the hub. The centre of each bolt is
75mm from each of the other two (i.e. they form an equalateral
triangle).

Dredging up my schoolboy trig, I've calculated that the effective
radius from the centre of the wheel hub to the bolt holes is 43.3mm.
Anyone care to confirm, or correct? Please show your working...
--
Champ

ZX10R | GPz750turbo | GSX-R 600 racer
My advice as your attorney is to buy a motorcycle
To email me, neal at my domain should work.

 

I get 45.92 mm

Working to follow.

 

I get 45.92 mm

Working to follow.

 

Split the triangle into two right angle triangles with sides 75, 37.5
and 64.95 (pythagorus)

The centre of the wheel is halfway along the 64.95 side.

The new right angled triangle formed from the centre has sides of 37.5,
64.95/2, and the radius, which from pythag again is sqrt((64.95/2)^2 +
37.5^2) = 49.6

Arse.

Yet another answer.

 

I agree.

http://homepages.gotadsl.co.uk/~deguello/ukrm/07042008053.jpg

 

Equilateral triangle has all angles = 60 deg
Your required length (r) is the radius hub centre to any bolt, so draw
a line, which will disect the angle, giving 30 deg. Extend one of the
other radii to make a right-angled triangle, disecting your known
length, therefore producing a triangle with one side 37.5 mm and a 30
deg angle.

So using the old SOHCAHTOA, where Cos=Adjacent/Hypotenuse
you'll get
cos(30)=37.5/r
r = 37.5/cos(30) = 43.301

--
_______
..'_/_|_\_'. Ace (brucedotrogers a.t rochedotcom)
\`\ | /`/ GSX-R1000K3 (slightly broken, currently missing)
`\\ | //' BOTAFOT#3, SbS#2, UKRMMA#13, DFV#8, SKA#2, IBB#10
`\|/`
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I'll get me coat.

 

Using the patented Mavis Beacon "Hunt&Peck" Technique, Champ

Are you certain about that 75mm? Only 43.3 is an odd sort of number.

 

Halfway along? <marks down>
--
Champ

ZX10R | GPz750turbo | GSX-R 600 racer
My advice as your attorney is to buy a motorcycle
To email me, neal at my domain should work.

 

AutoCAD says you're right.

 

43.30 as drawn in Autocad

 

You could use

http://www.1728.com/indextrg.htm

43.301

--
Paul - xxx

'96/'97 Landrover Discovery 300 Tdi 'Big and Butch'
'98 Suzuki DR 200 Djebel 'Small but perfectly formed'
Dyna Tech Cro-Mo comp "When I feel fit enough'

 

So does Microstation

 

It is, isn't it. The three bolts had dished heads, so Keef just stuck
the verniers into bolt head. Could easily be +/- 1mm out.

If I were getting something made, that would be disastrous, obviously.
But, in fact, I'm just trying to describe what I've got so I can get
another one the same off the shelf, so it should be good enough for
these purposes.

--
Champ

ZX10R | GPz750turbo | GSX-R 600 racer
My advice as your attorney is to buy a motorcycle
To email me, neal at my domain should work.

 

Sorry sir, I'll try harder next time.

 

If you work backwards from a radius of 42 you would probably get the
correct bolt spacing and the meaning of life...
--
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Agree

I've constructed it on CAD and the circle works out at 86.603mm

Steve

 

Yeah, that's nice and easy to remember. What are 'B' and 'P' supposed
to stand for anyway?

--
_______
..'_/_|_\_'. Ace (brucedotrogers a.t rochedotcom)
\`\ | /`/ GSX-R1000K3 (slightly broken, currently missing)
`\\ | //' BOTAFOT#3, SbS#2, UKRMMA#13, DFV#8, SKA#2, IBB#10
`\|/`
`

 

Base and Perpendicular?

--
Ivan Reid, School of Engineering & Design, _____________ CMS Collaboration,
Brunel University. Ivan.Reid@[brunel.ac.uk|cern.ch] Room 40-1-B12, CERN
GSX600F, RG250WD "You Porsche. Me pass!" DoD #484 JKLO#003, 005
WP7# 3000 LC Unit #2368 (tinlc) UKMC#00009 BOTAFOT#16 UKRMMA#7 (Hon)
KotPT -- "for stupidity above and beyond the call of duty".

 

OIC. Somehow not as intuitive as Opposite, Adjacent and Hypotenuse.

--
_______
..'_/_|_\_'. Ace (brucedotrogers a.t rochedotcom)
\`\ | /`/ GSX-R1000K3 (slightly broken, currently missing)
`\\ | //' BOTAFOT#3, SbS#2, UKRMMA#13, DFV#8, SKA#2, IBB#10
`\|/`
`