Help solve complex math problem... reward if found.

[Ischgl99]

I know where the .705" is from. That's the outside diameter of the bolt nose. If you had the action in hand, that is where you would check the bolt nose clearance with plastigauge or a piece, small diameter solder or lead squirt.

I was wondering how they came up with that measurement, it was 0.002” off from a 1-13/32” ball, so I was scratching my head why it didn’t correspond to any standard gage balls I found that would make the measurement easy.

 

[xr650rRider]

The tenon diameter for the Remington 700 clones is usually max 1-1/16", so 1" ball is all that's going to fit in the tool. That 1" ball was mostly used for duplicating cone bolt 6 PPC barrels.

 

[rwm]

I can. See post #9. 1.41 dia ball is tangent at .705. Its a 2:1 ratio. because sin of 30 degrees is 0.5.

Yes, You are cleverly correct on this. A sphere can only contact an inverted cone at one specific diameter. I made the fundamental mistake of assuming the OPs numbers were correct.

 

[jwmay]

Thank you all for a close up look at how you all go after a solution. That was impressive!

 

[3strucking]

If the point-of-contact is at 30 degrees to vertical, and you know the point-of-contact to flange distance,
A to B will be
( (0.705/2 ) * (1 + sin(30 degrees) )+ (0.814 + .001 to 0.814 -.003)
sin(30 degrees), of course, is 1/2

The place to start, is to note that the sphere is tangent to the cone at the point of contact,
so that's a right angle between the radius to the point of contact and the slant surface.

That was like me trying to read Chinese. I sure wish I had paid better attention to math in school.

 

[Just for fun]

You and me both!

 

[LVLAaron]

Why can't you measure off of a headspace gauge? Have you finished the chamber yet, or are you doing the cone first?

Ideally, I'd like measurements/instructions like Kelbly has (see my previous post link) - Basically, move right "this far" from the shoulder and cut your cone with the compound. I can get it figured out once I have an action in hand.

This all spawned because I have a friend in need of a quick turn-around barrel and isn't in a position to send me the action

 

[whitmore]

If the point-of-contact is at 30 degrees to vertical, and you know the point-of-contact to flange distance,
A to B will be
( (0.705/2 ) * (1 + sin(30 degrees) )+ (0.814 + .001 to 0.814 -.003)
sin(30 degrees), of course, is 1/2

The place to start, is to note that the sphere is tangent to the cone at the point of contact,
so that's a right angle between the radius to the point of contact and the slant surface.

Oops; I was misreading the sphere radius (above should be 1.000/2, instead of 0.705/2) and
maybe the angle " 30 degrees to vertical" should have been '30 degrees to horizontal ?

 

[xr650rRider]

Ideally, I'd like measurements/instructions like Kelbly has (see my previous post link) - Basically, move right "this far" from the shoulder and cut your cone with the compound. I can get it figured out once I have an action in hand.

This all spawned because I have a friend in need of a quick turn-around barrel and isn't in a position to send me the action

Isn't that what Borden is giving you? Tells you your tenon length is 0.9", headspace is 0.9", so headspace gauge would be flush with back of tenon when chambered to proper depth. It tells you at .705" diameter, you should be 0.814" away from shoulder. You know the angle is 30 degrees. A hint is that if you project that 30 degree angle from the .705" diameter and .814" measurement to 0.9", the diameter is 1.003". So you'll have a small flat from tenon OD to 1.003" diameter and that's where the cone begins. Always good practice to set compound to mid-travel, zero dial and make a mark, so you can get back to your zero reference. Use cutter, your cutting cone with and get an accurate diameter and distance from shoulder. Now this gives you a Borden spec barrel, that should fit but if somebody has "tuned" it, you never know.

 

[LVLAaron]

I'm criminally bad at math, let me get that out of the way. If I follow what you're saying.

Lock compound at 30 degrees.
Cut tenon w/ DRO set correctly for X and Y.

Come over .900 from the shoulder
Move cross slide in, to 1.003
Use compound to cut cone