Tom Myers wrote on Aug 3^rd, 2016 at 7:20pm:


Tom,
Welcome to the forum.

Frank

Tom,  You amaze me with your application and your ability with calculations.  Frank too.

Would seem from your findings with the new release that 5 more gr of black powder would require considerably more compression ‘or’ cheating the bullet out as has been suggested.    For now I’m in Oklahoma and my 35-40 in Idaho, along with brass and OE.   But I’ll be sure and measure the difference in the column height between 40 and 45gr when I get back in a couple weeks.   

Given that degree of compression could adversely impact accuracy it seems like flexibility in seating depth might be prudent through being a newcomer I’m a little skittish about having just a ¼” in the case.   That’s just a comment about me, not the common practice for more experienced BP shooters.      

Beltfed’s recommendation “3rd from base, use the 3 degree taper here .357  to 0.349”, gets to another lacking on my part.   I don’t see how with the software you can create a taper on any of the midway bands.   I only see that option for the front band, which means you’d have to accomplish Frank’s 1.54* angle (post #20) with a two graduated bands, similar but to Beltfed’s offering.   So back to establishing the desired degree at a given spread between those two bands (reduced to four in this drawing).   Bottom line, I don’t know the formula Frank and you used to arrive at the desired degree created by those two bands.   

Lets say I wanted to compromise on a starting seating depth of 3/8” and achieve the following:
*A short bore riding section on the nose as with Tom’s drawing.
*Tapered bands to create the 1.5 angle given the distances.
*The longer base band and shallower lube groove diameter.
*All for some flexibility in seating depth.

My first question would be about the actual degree desired.  Is it a 3* or a 1.5* based on the chamber reamer spec?  I.e., is that 3* an included degree (reply #1)?
And what size would the two reduced driving bands be to obtain the desired angle (or what formula would I use)?   
Note:  the two diameters for the reduced driving bands are just place holders in this drawing since I don’t know how I’d arrive at accurate diameters here.

PS – I appreciate your hanging in there as I gnaw over-long on this bone.   

John,
As a machinist, I had to learn trigonometry. Trig is what I use to solve all problems having to do with angles.

If you have a "scientific" type calulator, it will have buttons for sin, cosin and tan. Tan will be the most useful for this.

The Tangent of a 90 deg angle is nothing more than the height of the angle, divided by the length of it.

The tan of 3 deg is .0524, that means that for every 1" the heigth will increase by .0524 if your leade is .124 long, the leade will increase by .0065 in that .124 length, per side or .013 included.

If I wanted to put a band in the middle of that area, to match the leade, it will have to be 1/2 that dia at 1/2 the length or, .0065 larger in dia at .062 from the start of the taper.

You also have to take in to account 1/2 of the width of the band but, for your band width and your alloy, that area will engrave w/o a problem.

I hope that helps.

Frank

BTW, your leade angle on the reamer drawing is 3 deg per side or 6 deg total.

SgtDog0311 wrote on Aug 5^th, 2016 at 11:27am:
 

You would need an additional 0.19 inches of compression to retain the same seating depth. 


Quote:


You can estimate small angles such as leade angles without using trigenometry.

To do this, subtract the bore diameter from the groove diameter and divide the result by the length of the leade and then multiply that answer by the constant 57.3. to arrive at the included angle. Then divide that by 2 to arrive at the leade angle.

This works pretty good for angles up to about 5 degrees.

Groove Dia. = 0.357"
Bore Dia    = 0.348"
Leade Length = 0.086"

0.357 - 0.348 = 0.009
0.009 / 0.086 = 0.1047
0.1047 x 57.3 = 6
6 / 2 =  3°  leade angle


Quote:


Most of the time, leade angles are referenced as the angle formed by the slope of the tapered lead in relation to the axis of the bore. is this case, the leade angle is 3° or a 6° included angle.

Quote:


This might fit those requirements.

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Ok,  One final note I think is of interest.   At least to me.

If you look at Tom’s chamber (reply #34) it takes a couple things into account from the Manson reamer diagram that would impact dimensions yet not jump out at you from that reamer diagram.

-The 45* step takes up a length or distance at least equal to the brass thickness (approx.)  .0095 in this case.

-Then there is essentially a cone or funnel noted as freebore where the same 3* (unless specified otherwise) is cut, from the .360 diameter at the end of the 45* step, to the groove diameter of .357.  That distance is another .0383.

-The leade is shown in length to be .0895 and begins at what is here identified as the freebore.

-The throat for purposes of his software encompasses all three and is .1240.

Doesn’t change anything here but I find that all pretty interesting since those together might impact how far out you actually want some driving bands of specific diameter.   And if ideally you want a lube groove showing at the end of your step seems like a good idea to walk the numbers in from both both directions.    

Regarding my original "quasi-Money bullet" proposal Finally got a chance to play with numbers regarding the bullet stability in my  14" twist TJ liner.

Here is what I have for the mold being made now by Brooks.    Hope there is some fudge factor here.

First,  I used constant of 150 with this formula:

Twist = 150 x diameter sq'd / Length
Or
150 x .127449 / 1.250 = 15.29 twist
 
Next, using what I read from Lee Shavers in the "Single Shot Exchange" for a better swag at the constant (135) or generally speaking the  SqRt of velocity,  I get the following:

135 x .127449 / 1.250 = 13.76 Twist

If I do the actual SqRt of 1300fps I get a constant of 126, which gives some concern in my 14 twist liner:

126 x .127449 / 1.250 = 12.84

Knowing the bullet length and twist being used by some successful shooters I'm a little surprised and skeptical --  here's to hoping the first calculation is the better indicator.   

John,

As I understand it, stability is a function of length.  That is why heavy-for-caliber JSP bullets tend to be round nosed instead of spitzers - keeps the bullet shorter and easier to stabilize when pushing the limits of twist.

Thanks for the input John and Hiwall,   Guess the proof will be in the pudding.    Looks like I'll need to hang some paper on a frame and examine holes once I cast some.    I'm not opposed to smokeless.    But I'll give what a case will hold in Black a try first.    Mold should be ready about the time I return to OKLAHOMA in three weeks.  Always a chance the constant of 150 is the better variable in the equation.