The Bradshaw Scale

This should be a simple one and probably gets repeated at least once a year.

Treat me like the novice I am, could someone explain the Bradshaw Scale for me?

Hope this is still accurate:

 

The Caber

The caber is done a little bit differently. Each caber is assigned a value. First the "Taper Factor" must be calculated. Take the distance from the large end to the center of gravity, call this A. Take the distance from the small end to the center of gravity, call this B. The taper factor is then A/B. This gives an idea of the taper of the caber. To calculate the value of the caber, multiply the length in feet of the caber times the weight in pounds times the Taper Factor times 0.55. This is the value an athlete gets if he/she turns the caber at 12:00. For anything less than this, 0.6 points/minute is subtracted. If the athlete does not turn the caber, but receives a score in degrees, 3 hours (or 108 points) is removed from the score, and this new number is now multiplied by (score in degrees)/100.

Example: Let's say we have a caber that is 20 feet long, 110 pounds, and the center of gravity is 8 feet from the large end.

• Taper Factor = 8/(20 - 8) = 0.667
• Value of caber = 20 * 110 * 0.667 * 0.55 = 807 points
• Therefore, a 12:00 throw = 807 points
• a 10:30 throw = 807 - 90 * 0.6 = 753 points
• a 70 degree throw = (807 - 108) * 70 / 100 = 489 points

Height	Weight	Taper	.55	Points
20	110	.667	.55	807.07

Right:  now, with all that said, I have my doubts that the formula really rates the difficulty of turning a given caber.

For example, the main caber we used at MWC last year (my #4) rates 790 on the Bradshaw scale, a rating I thought should be manageable by most of the under-50's (based on my experience with similar-rating natural cabers).  At MWC, only a minority of the 40-44 year class turned it (8 of 17), and only 2 of 10 of the 45-49 year class*.  This stick is relatively untapered (its taper factor is all of 0.88), and long (19'2") for its relatively light weight (85 lbs).

I've been toying with an analysis that should demonstrate whether or not the rating really reflects the difficulty of turning a caber, but it's very time-consuming and I haven't really gotten that far with it.

-Wayne
________________________
* Funny story:  one of the 45-49 year class athletes took one look at it and said it was too light, and would lead to a shoot-out.  Bill Crawford said, "Well, if it turns out to be too easy a caber, we'll call it a qualifier and move on to a tougher stick."

I've thrown many a caber in my time and I've found that I ALWAYS have trouble with the longer cabers.  I can turn a 15' 150 lb caber but I have the damndest time with a 20' 90 lb stick.  I've not done the calculations on these so I don't know what they would score on the scale.  It has always seemed to me that there are more forces that need to be taken into consideration to score a caber.  Physics was never my best subject (so why the hell am I thinking of math and physics on a Friday night- man I need a life), but wouldn't the distance through an arc come into play with longer cabers?  Which variables are easiest to change- vertical thrust (strength) or horizontal velocity (speed)?  Consistency of the ground also comes into play- mud, sand, hard earth.  OK, these can't be calculated into a caber.  These are just a few questions that come to mind when thinking of cabers and how the hell  am I gonna turn them.

Wayne Hill wrote: ...I have my doubts that the formula really rates the difficulty of turning a given caber...I've been toying with an analysis that should demonstrate whether or not the rating really reflects the difficulty of turning a caber, but it's very time-consuming and I haven't really gotten that far with it.

I've been wishing two things; that someone out there would perfect that formula (I read a lot of bio's from athletes who've been to college), and that NASGA would use it when ranking athletes (good caber tossers get the short end of the stick)!

We use Greg's formula at Enumclaw but we also keep track of how well each caber was turned last year and use that in the mix.


Edited by wallyworld

Kirk,

I certainly don't mean to denigrate the Bradshaw scale, since it's a serious attempt at doing something that I think is very worthwhile.  It should certainly continue to be used until something better comes along.  From my preliminary efforts, it doesn't look easy to come up with a better rating scale.

What's throwing me off is the fact that my 790 caber seems to be a heck of a lot harder to turn than other cabers of similar or higher ratings.

-Wayne

Tim wrote: I've thrown many a caber in my time and I've found that I ALWAYS have trouble with the longer cabers.  I can turn a 15' 150 lb caber but I have the damndest time with a 20' 90 lb stick.  It has always seemed to me that there are more forces that need to be taken into consideration to score a caber.

Any current or potential formulas will have flaws based on the bias of the creator. In addition, in order to consider the variables, the complexity would become challenging for non-math people. In the Bradshaw, the taper is the key factor with height and weight being "equal" in their consideration. However, with a balanced caber (centerpoint is center of gravity) a 30ft 100lb caber is of equal value as a 10ft 300lb caber. While I am not a seasoned caber turner, I would argue the challenge level of a caber is not linear.

Tim does address a good point. At what height, weight, or other consideration does a caber become more challenging to turn? Consider height alone, is a 24ft caber more challenging than an 22ft, a 22ft more challenging than an 20ft, a 20ft more challenging than an 18ft?

Edited by Eclipse

I agree Ed, and you have illustrated my question well with your 17' answer. Does the challenge become exponential beyond x ft? Unlikely, but it does need to be considered with greater emphasis than a shorter caber.

Only thing needed is a bunch of data points that have

Length, Weight, Taper, # who tried to turn it, # who turned it, class

I think then a person could use the data to modify the breakpoint (15 feet) and the multiple (2) to get perhaps a better formula. 

This formula is not based on some physics calculation -- It is a simple way of taking into account that longer cabers are harder to  turn.   Given that I pulled 2 and 15 out of my arse, I would assume that as parameters to an equation, they stink!  Math humor?

Edited by McSanta

I agree that peice wise does not have elegant mathematical properties --

I do like the proportion to moment of inertia

I am assuming then M = Mass or weight

To take into account the taper of the caber, I am assuming that
L then is the distance from the large end to the center of mass?

or using the notation from Bradsaw formula:

A = The distance from the large end to the center of gravity

Moment Formula = 0.1389 * Weight * A^2

0.1389 was the value to Make your 19'2" , 88# caber score a 950 so that it is comparable to the two peice formula

Length	A	B	Weight	Taper	Moment (large to center)	Two Piece	Bradshaw
21.00	9.830	11.170	85	0.88	1140.8	1110.8	863.9
20.50	9.596	10.904	85	0.88	1087.1	1069.6	843.4
20.00	9.362	10.638	85	0.88	1034.7	1028.5	822.8
19.17	8.972	10.195	85	0.88	950.3	959.9	788.5
18	8.426	9.574	85	0.88	838.1	863.9	740.5
17	7.957	9.043	85	0.88	747.6	781.7	699.4
16	7.489	8.511	85	0.88	662.2	699.4	658.2
15	7.021	7.979	85	0.88	582.0	617.1	617.1
14	6.553	7.447	85	0.88	507.0	576.0	576.0
13	6.085	6.915	85	0.88	437.2	534.8	534.8
12	5.617	6.383	85	0.88	372.5	493.7	493.7
11	5.149	5.851	85	0.88	313.0	452.5	452.5
10	4.681	5.319	85	0.88	258.7	411.4	411.4
17.00	5.667	11.333	100	0.5	446.0	522.5	467.5
17.00	6.375	10.625	100	0.6	564.5	627.0	561.0
17.00	7.000	10.000	100	0.7	680.6	731.5	654.5
17.00	7.556	9.444	100	0.8	792.9	836.0	748.0
17.00	8.053	8.947	100	0.9	900.7	940.5	841.5
17.00	8.500	8.500	100	1	1003.6	1045.0	935.0
30	14.043	15.957	100	0.88	2739.0	2178.0	1452.0
10	4.681	5.319	300	0.88	913.0	1452.0	1452.0

Is a 17' stick weighing 100# with no taper equally or slightly harder to turn then your 19'2" stick used at MWC?

I also believe that if a formula is to be calibrated, The score of 1000 should have some meaning in that it is damn hard to impossible for mear mortals to turn OR perhaps use some of the measurments from the historic Braemar Cabers that are in Highland games legend:

An  X pound caber with Y taper that is Z feet long would generate 1000.

I have not turned enough cabers to say what a 1000 caber should be.

No matter what is used as 1000 score, I think Mr. Wayne Hill's idea is a much better caber formula than the others.

Edited by McSanta

McSanta wrote: I do like the proportion to moment of inertia I am assuming then M = Mass or weight

Yep, but note that we have the advantage of living in a 1-g world (apart from the gravity anomaly we discovered at the Glasgow Lands games).  The weight of the caber matters, because that's what you have to lift, but the mass (distribution) also matters, because this is what we have to turn in the air.

To take into account the taper of the caber, I am assuming that L then is the distance from the large end to the center of mass?

All right, here's another of the things that are working on me here:  when you turn the caber, its center of mass is allowed to fall by the difference between the distance from the top to the CM and the distance from the bottom to the CM.  This is the advantage of a tapered caber.

or using the notation from Bradsaw formula: A = The distance from the large end to the center of gravity Moment Formula = 0.1389 * Weight * A^2

You're on the right track, but this is assuming a uniform caber.  A tapered caber has a higher moment of inertia for its weight and length.  I suspect that knowing the weight, length, and balance point will allow an estimate to within 5% or so, but that will take some doing.

No matter what is used as 1000 score, I think Mr. Wayne Hill's idea is a much better caber formula than the others.

Oh, no you don't, wise guy!  It's not a formula yet:  we've just described the problem.

-Wayne

Wayne Hill wrote: McSanta wrote: No matter what is used as 1000 score, I think Mr. Wayne Hill's idea is a much better caber formula than the others. Oh, no you don't, wise guy!  It's not a formula yet:  we've just described the problem. -Wayne

Well okay I tried and If I was making the post now, I would have said I am starting to see the framework of a better formula because I am now seeing the complexity of the problem -- For once in my life I wish I took Physics with all my math because I am on a very steep learning curve. 

However, if one can mathematically quantify the forces at play, would it not be wise to use an approximate and hopefully simpler formula in the application?

 

Edited by McSanta

McSanta wrote: For once in my life I wish I took Physics with all my math because I am on a very steep learning curve. However, if one can mathematically quantify the forces at play, would it not be wise to use an approximate and hopefully simpler formula in the application?

Forces can be identified, however, to be quantified additional variables enter for consideration. If forces are to be considered within a formula, they would need to be done in a neutral environment (lack of wind, etc).

We can make the games so complex that they begin to lose their appeal, somewhat anyway.

I like what I named, years ago, the California System.  Why that name, because that's the first place I ever ran into it.....

1 Caber per class, three throws,  ALL THROWS COUNT.  Finish the caber and move on. 

If the throwers want more or the crowd does, have a Challenge Caber.

When we did decathlon scoring, we needed computers, and a good program to not only calculate the caber points, but keep track of the standings and overall points.

If the cabers had not been scored prior to the games, someone had to determine center of gravity, distance to top, bottom, equations, weights, etc., and then document all this.  And, if you are totally legit, cabers change from year to year and perhaps, even game to game, so a repeat of the process may be needed.

I, for one, want the game to be done in the best, most simple format possible.  I prefer to spend my game day hanging with the guys and gals, throw, hopefully far, but just have a great day being Scottish for a day.

When I started they told me there'd be no math

I have no particular attachment to the caber rating for the score within a specific game, but having a caber rating available allows for comparison to other athletes across the country, even though they may never see each other.

Note, I am not comparing myself, that's easy, I lose.  But it helps me to understand what sort of competition is out there.

And, I like the math.