Another Physics Brain Teaser

I've lost something...

Dear Danish:

Regarding what I have lost:
Where it is now, might not be where it might be found 5 minutes from now as someone could indeed pick it up ! And someone else after him !

As for you Jack me boy, if you have read the above then you know that it might not be where I lost it... but, where will "I" find it.

As for you guys living in shoe boxes and holes, count yourselves lucky because as you can see in his picture "The view out of the door", our dear Raggi Thor lives in a snow cave

 

Question about a radius

Allright everyone... this doesn't qualify as a brain teaser or even a riddle but, having read all the posts in this thread, I believe that you are the fellas to answer my question. I've got to cut new beams for the roof of my cabin. They have an arch or radius. The old beams are cracked and warped not to mention mis-shapen due to someone elses work in the past but, non the less, I don't want to use them to trace the new beams shape if I don't have to.

Included is a picture of a circle with a couple of dimensions on it. Can you caculate the radius from these two dimensions ? If so, can you include the formula to do so... so that I can caculate the other two beams as well.

I'm not exactly an idiot... I used to work with triangles and radius' years ago but, my geometry really isn't what I wish it was.

Thanks.......

P.S.
The answer to my question earlier is...."The LAST place I look"

 

Err you mean 'the last place you look for it', dont you?

You look to live in a nice little town, is that a church there? I would imagine that to be a safe place. Ive never been to America as I dont want to get shot but your place looks nice.

Ive always fancied riding a Harley accross America but ide be a bit worried about those dusty cafe's where when you walk in the piano player stops playing and every one turns to look at you. Then the bartender says " wes dont go in fur them ther strangers rounds here mister'.

Is there any way of avoiding those places. Hey perhaps we could get a Boat design . net forum ride, then we could get the crazy guys off the pirate thread to protect us.

Actually Im serious about this idea. Any body?

 

Jack me boy ! I think that shovel stuck down yer boot would get in the way on that harley, then again... it might come in handy as your navigating your way around one of those dusty cafe's either for protection or to dig someones grave... hopefully not yer own

As for the seriousness of a BD.net ride... My 18 speed mountian bike won't keep up with the rest of your guys' harleys.

Having been a truck driver for over 20 years now, I've seen the entire country many times over thru a windshield... but, it sure would look great from the seat of a low rider............................ if I had one !

 

"Is there any way of avoiding those places"

Wouldn't it be enough to just print out the pirate thread and circulate it in pirate infested areas? That should put off all pirates having less than rocket propelled granades and Browning 50s' from attacking

Mikey

 

Virkrue( shovel inth boot) does not mean a shovel in your boot. In American it means a shovel in the trunk of your car. Yes we call it a boot and a hood is a bonnet---wierd hey?

Your experience of the road maps would be handy. You could ride ahead and stop the traffic and direct us left or right. You could also warn the dusty cafes that Englishemen were coming. Not quite sure what they would do about that but! Warn them any way. Oh maybe put a couple of cans in the sun-- we like it warm?

Rent a Harley like the rest of us would have to. There are companies that specialise in this. Pick up New York and drop it in erm -erm some where else.

 

VCRUE - I don't know if you seriously want to do this radius bit or just testing our mathematical ability.

Since I don't have any mathematical ability (or any other) I would:
1. Mark out a "Tee" with the top of the Tee 54" across.
2. From the top of the top mark out 2 1/2"
3. If you do it on the ground you can use a tent peg a piece of string and a pencil.
4. Tis the tent peg to the string at one end and the pencil at the other and keep moving the peg down and lengthening the string until the pencil scribes an arc through the 3 points.
5. When you have the aproximate lengths, do it again with a timber tee piece using the string with a nail at one end and the pencil at the other.
6. Lay your timbers on the top of the tee piece and mark them out with the pencil.

Or - Not giving the same arc but similar results ie marking out a curve. Place 2 nail on a piece of timber 54" apart with 2 1/2" slack in the string and run a pencil along the string pushing outwards one way. The pencil will follow the slack in the string and draw an arc.

OR - Draw out the Tee etc. on a piece of graph paper by scaling down the size. When you find the arc that bisects all 3 points, draw another grid larger that the grid on the graph paper by the scaled amount, on a piece of ply. Plot the arc using the co-ordinates from the graph paper onto the larger grid. Join the dots, you have the arc, cut it out and you have a template.

OR - Sell your boat and buy a new one.

Poida

 

If the offset on your drawing is 2 1/2 inches (a little unclear on my monitor) then the radius is 12ft 3 inches.

I'm afraid I can't tell you how I did it as it's still restricted information under the provisions of our Official Secrets legislation, specifically the 'Aid and Succour' clause of the Abbetting Uppetty Colonies Act, of 1774.

However, if you let us have the other measurements I'll work them out for you, no bother.

Oh okay, I used the three point circle command you find in any CAD package.

 

Vic, I thought you had lost your mind
But how do you find that again?
Or your temper?

Regarding circles.
If you have a cad program, that is often easier than looking into a german collections of formulas

 

Formula

This is from my college teacher
Look for congruent triangles...
You have an arc with a cord length L and a height h.
If h is much smaller than L calculations can be simplified, because if Alfa is small, Sin (Alfa) ~Tan (Alfa) ~Alfa.

We'll just use Pythagoras on the largest triangle.
R^2 = (R - h)^2 + (L/2)^2
After some playing around at the drawer we see (easily as the teacher used to say) that
R = L^2/8h + h/2
In your case
R = (54^2)/(8x2.5) + (2.5/2) = 147.05

 

Yeah Raggi Thor

That was method 7 I was going to use but I didn't want to show off.

LIKE SOME PEOPLE!!

 

Deck camber exactly

The attached is the exact answer.

"a" = height of camber
"y" = half breadth of the beam
"r" = the radius of the circle for the deck camber

This shows the derivation of the formula, and you can set this up into a spreadsheet to calculate the radius of camber for any given beam and camber height.

Eric

 

I wasn't clear enough.
If h<<L you can skip the h/2 part and simply say
R ~ L^2/8h
in all cases
R = L^2/8h + h/2 (exact I think)
Eric,
Using both tan an arctan may be more fun, but also more work

 

But that is the nice thing about boat design and engineering in general, a discrete equation gives an exact answer. And I don't think this is necessarily hard.

Eric

 

Take no offence, but I think your formula is harder to use than mine
Some small "calculators" don't even have tan and arctan, but al can do
54 x 54 / 8 / 2.5