## Formulas and tech details

## Angle of Attack of Broadheads

In his 2007 Study Update, Part 7, Dr. Ed Ashby discusses angle of attack of broadheads and what it actually means to the archer. It is a simple read and the calculation is simplified with his explanations.

The main thoughts have been either quoted or paraphrased below:

*“The angle of attack of a broadhead is the slope each cutting edge presents to the tissue as the broadhead penetrates. For a single-blade broadhead the attack angle equals one-half the total angle formed by the blade's edges. All else equal,
the lower a blade's angle of attack the more effortlessly it passes through the tissues, conserving arrow force. It's precisely like a car driving uphill; the steeper the hill the harder the car has to work to get up it, and the more energy
that’s expended in doing so.” *

The angle of attack can be calculated on a
computer CAD program, but there is a simpler method that most
can do using just common tools. For concave and convex
broadheads there will be some estimate of the average angle of
the blade to the broadhead’s center line. For these broadheads
you will have to settle for an approximation. For broadheads
having straight-taper blades the simple-tool method is almost as
accurate as a CAD program. Here is the method:

(Accuracy of the results are dependent on the accuracy of the
measurements and how precise the lay out.)

1. On a piece of paper make a horizontal line.

2. Construct a second line perpendicular to the first. Extend
the line above and below the horizontal line.

3. Take the measurement of the subject broadhead. The
measurements needed are:

a. the cutting width at the
blades widest point and

b. the overall length of the broadhead (OAL).

If the tip profile differs, measure how far back tip profile
ends and the width where it terminates.

A. With these measurements you can lay out the broadheads shape
so that the widest point of the blade falls on the horizontal
layout line with the broadhead’s ferrule and tip centered.

B. Mark the broadhead’s width on the horizontal line. If the
broadhead is not a straight taper, mark on the bottom half of
the vertical line how far below the blade’s greatest width the
back end of the ferrule falls.

C. Using the OAL, mark the location of the broadhead’s tip on
the upper vertical layout line.

D. Starting from the top, mark the overall length (OAL),and also
mark both the location and width at the rearward ermination of
any tip profile.

E. Using these reference points make a straight line starting at
the widest blade mark on one side of the horizontal layout line
passing through the tip profile's width mark (for that side of
the broadhead) and stopping at the vertical layout line.

The result is a right triangle. The angle formed at the top of
this right triangle represents the angle of attack of the
blade's cutting edge.

F. At this point you can measure the angle of attack with a
compass. Measure the supplementary angle and subtract it from
180 degrees to derive the angle of attack.

G. A more accurate way to do it is to calculate the angle.

To calculate the angle of attack you'll

1. First measure the "Extended Length" of the blade; the distance from the intersection of the horizontal and vertical layout lines to the point where the line from the widest cut mark intersects the vertical layout line. The "Extended Length" compensates for any difference between the angle of attack of the tip and the blade's angle of attack.

2. Now calculate the angle's tangent To find the tangent of the angle of attack divide one-half of the blade's widest cut-width by the "Extended Length". For example, if the blade is 1.5" wide at its widest point and the "extended length" is 3" divide 0.75 (half the cut width) by 3. The resulting number, 0.25, will be the tangent of the angle.

3. The last step is to look up the
tangent number to see to which angle it corresponds. For your
convenience a tangent table has been provided.

How we compute TuffHead's™ Angle of Attack

Length of line AC ( OAL ) = 4.25”

Length of line AB ( ½ of width of blade ) = 1.0625/2 = .53”

C= Line AB (½ x width of blade) ÷ Line AC (OAL) = .53"
÷ 4.25"

C=.12

Looking at the tangent table below we see that the tangent angle is
approximately 7 degrees.

therefore, TuffHead's
Angle of attack = 7 degrees

Enter your broadhead's details and then use the tangent table below to find its Angle of Attack

Angle | Tangent | ° ° | Angle | Tangent | ° ° | Angle | Tangent |

0 | 0.0000 | 30 | 0.5773 | 60 | 1.7317 | ||

1 | 0.0175 | 31 | 0.6008 | 61 | 1.8037 | ||

2 | 0.0349 | 32 | 0.6248 | 62 | 1.8804 | ||

3 | 0.0524 | 33 | 0.6493 | 63 | 1.9622 | ||

4 | 0.0699 | 34 | 0.6744 | 64 | 2.0499 | ||

5 | 0.0875 | 35 | 0.7001 | 65 | 2.1440 | ||

6 | 0.1051 | 36 | 0.7265 | 66 | 2.2455 | ||

7 | 0.1228 | 37 | 0.7535 | 67 | 2.3553 | ||

8 | 0.1405 | 38 | 0.7812 | 68 | 2.4745 | ||

9 | 0.1584 | 39 | 0.8097 | 69 | 2.6044 | ||

10 | 0.1763 | 40 | 0.8390 | 70 | 2.7467 | ||

11 | 0.1944 | 41 | 0.8692 | 71 | 2.9033 | ||

12 | 0.2125 | 42 | 0.9003 | 72 | 3.0767 | ||

13 | 0.2309 | 43 | 0.9324 | 73 | 3.2698 | ||

14 | 0.2493 | 44 | 0.9656 | 74 | 3.4862 | ||

15 | 0.2679 | 45 | 1.0000 | 75 | 3.7306 | ||

16 | 0.2867 | 46 | 1.0354 | 76 | 4.0091 | ||

17 | 0.3057 | 47 | 1.0722 | 77 | 4.3295 | ||

18 | 0.3249 | 48 | 1.1105 | 78 | 4.7023 | ||

19 | 0.3443 | 49 | 1.1502 | 79 | 5.1418 | ||

20 | 0.3639 | 50 | 1.1916 | 80 | 5.6679 | ||

21 | 0.3838 | 51 | 1.2347 | 81 | 6.3095 | ||

22 | 0.4040 | 52 | 1.2798 | 82 | 7.1099 | ||

23 | 0.4244 | 53 | 1.3269 | 83 | 8.1372 | ||

24 | 0.4452 | 54 | 1.3762 | 84 | 9.5045 | ||

25 | 0.4663 | 55 | 1.4279 | 85 | 11.4157 | ||

26 | 0.4877 | 56 | 1.4823 | 86 | 14.2780 | ||

27 | 0.5095 | 57 | 1.5396 | 87 | 19.0404 | ||

28 | 0.5317 | 58 | 1.6001 | 88 | 28.5437 | ||

29 | 0.5543 | 59 | 1.6640 | 89 | 56.9168 |

## Reference Room

- Dr. Ed Ashby and his Broadhead Lethality Studies
- Ashby .pdf's
- Ashby Jan 2012 Kalamazoo, MI
- Ashby May 2013

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