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Height of the hammer’s arc

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WALLY.OLECIK View Drop Down
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    Posted: 10/28/08 at 4:37pm
Now that the weather's going down the tubes, perhaps someone can help me out on a question l have.  What would be the height of the arc of a 16 pound hammer throw that goes, say, 135 feet?  This isn't just idle curiosity, we have a field that is rather short on one side and l'd like to know that the fence on that side is tall enuf to stop a long throw.  lt would be very cool if one of you brain types out there could break the arc down into heights at ten foot intervals from 100 feet on up.

Anyone??  lt would be very helpful and much appreciated.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote climber511 Quote  Post ReplyReply Direct Link To This Post Posted: 10/29/08 at 2:55am
I am not the brain type - but here's a guess.  The fence will be 1" to short to stop the hammer from going thru the windshield of the only Cadillac parked in the whole lot 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote WALLY.OLECIK Quote  Post ReplyReply Direct Link To This Post Posted: 10/31/08 at 12:22am
Wayne Hill?

McSanta??

(lt's not everyday that l admit to not knowing something so give a guy a little help!!!)
16lb-hammer(at)sshga.org

"Try not. Do or do not. There is no 'try!'" Yoda
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Wayne Hill Quote  Post ReplyReply Direct Link To This Post Posted: 10/31/08 at 2:44am
OK, OK, I've been busy and sick and stuff.

The issue here is the release angle.  I wouldn't mind if someone checked me on this, but (neglecting shoulder height) I get

Hmax = Distance * tan(theta) / 4

where theta is the release angle.  In a nominally optimal ballistic trajectory, theta would be 45 degrees, so tan(theta) would be one, and the maximum height would be one fourth the distance of the throw (33' 9", for a 135' throw).  In reality, because of the length of the implement, the release angle is almost always smaller, so the maximum height is less.  For a 40 degree release angle, which is a pretty high release for a Scottish hammer, the max height would be close to one fifth the distance of the throw (27', for a 135' throw).

Either of these is pretty darn high, so your fence probably isn't this high.  However, depending on the real setupof the field, it may well be that the fence doesn't need to be nearly this high (so tell us more).

"We may be small, but we're slow." - MIT Rugby
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Post Options Post Options   Thanks (0) Thanks(0)   Quote C. Smith Quote  Post ReplyReply Direct Link To This Post Posted: 10/31/08 at 3:40pm
I have hit a ceiling fan that was 35' or 40' with the 22lb. hammer at the Shamrock Games.  Kevin Rogers can verifiy.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Wayne Hill Quote  Post ReplyReply Direct Link To This Post Posted: 11/01/08 at 2:53am
It helps to have a target.
"We may be small, but we're slow." - MIT Rugby
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Post Options Post Options   Thanks (0) Thanks(0)   Quote WALLY.OLECIK Quote  Post ReplyReply Direct Link To This Post Posted: 11/02/08 at 9:43pm
Originally posted by Wayne Hill Wayne Hill wrote:

For a 40 degree release angle, which is a pretty high release for a Scottish hammer, the max height would be close to one fifth the distance of the throw (27', for a 135' throw).

(This) is pretty darn high, so your fence probably isn't this high.  However, depending on the real setupof the field, it may well be that the fence doesn't need to be nearly this high (so tell us more).

The way we're set up, we throw from the S.W. corner of the field aiming at the N.E. corner.  We have plenty of space except at the S.E. corner where the fence is just over 100' away.  The bleachers in this area are set high enuf that the crowd is looking over the fence which is 10' tall (l think).

So - what l'm reading is that this max height of 27' would be at the mid-point, or 67' 6" from the trig, down to 0' at 135".  lf l'm thinking in the right direction, the hammer would be about 14' feet off of the ground at 100'.  lf l'm close with the numbers, the hammer should not be more than about 10' off of the ground when it gets to the fence at between 100 and 120'.  Am l close??
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Wayne Hill Quote  Post ReplyReply Direct Link To This Post Posted: 11/03/08 at 12:22pm
The problem is that, at the top of the arc, the implement is traveling horizontally, so the path from there to touchdown starts flat and gradually steepens.  At 100', the throw with the 40 degree release angle (i.e, the lower throw) is still at 20'9"(!).

I'm not really sure how likely this is to cause a problem, though, because off-line throws usually aren't nearly as long as ones in the "sector".  The problem is the word usually...

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Post Options Post Options   Thanks (0) Thanks(0)   Quote WALLY.OLECIK Quote  Post ReplyReply Direct Link To This Post Posted: 11/03/08 at 11:53pm
Originally posted by Wayne Hill Wayne Hill wrote:

At 100', the throw with the 40 degree release angle (i.e, the lower throw) is still at 20'9"(!).  I'm not really sure how likely this is to cause a problem, though, because off-line throws usually aren't nearly as long as ones in the "sector".

This could be a real problem because our field record is 133'+ and if someone made a similar throw down that sideline, we could be in deep doo-doo!  Maybe l need to get someone (in better shape than myself) to make a few throws down the sideline with the 12# hammer to get some numbers so l can see how worried l should be.

Thanks for working the numbers for me.  l appreciate it.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Steve Conway Quote  Post ReplyReply Direct Link To This Post Posted: 11/04/08 at 2:33pm
Wouldn't the velocity of the hammer have something to do with the distance that it travels? I tend to agree with climber511; regardless of the height of the wall, the hammer will find a way to get over it   Always plan on the worst case scenario happening...
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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/08 at 5:47am

I can send you a spread sheet that will plot the trajectory of a hammer ignoring air resistance that is driven by input of : release angle and release velocity.

However, that probably will not give you what you want

I freely admit I am a math geek who avoided physics with utmost prejudice.  However, if you want statistical analysis or want average time to death or other actuarial calculation ...

 

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/08 at 11:21am

Assuming NO drag --- formulas from:

http://www.grc.nasa.gov/WWW/K-12/airplane/ballflght.html

t is time from release; x is horizontal distance; y is height

I have ignored the height of the thrower which will increase the distance a bit as well as the height.

Launch angle is 44 degrees which is close to optimal from what I can tell from the model -- biomechanical articles also indicate this

Launch velocity is 66.05 ft / sec^2 ---
Some of the best Olympic hammer throwers launch around 70 ft /sec^2  (based on some bio mechanical articles.  THis worries me as I am not sure whether those who can throw Scottish Hammers very well can approach the T&F's guys hammer release velocity ...

t x y
0.00 0.000 0.000
0.01 0.475 0.457
0.02 0.950 0.911
0.03 1.425 1.362
0.04 1.901 1.810
0.05 2.376 2.254
0.06 2.851 2.695
0.07 3.326 3.133
0.08 3.801 3.568
0.09 4.276 3.999
0.10 4.752 4.428
0.11 5.227 4.853
0.12 5.702 5.274
0.13 6.177 5.693
0.14 6.652 6.108
0.15 7.127 6.521
0.16 7.602 6.929
0.17 8.078 7.335
0.18 8.553 7.738
0.19 9.028 8.137
0.20 9.503 8.533
0.21 9.978 8.926
0.22 10.453 9.315
0.23 10.929 9.702
0.24 11.404 10.085
0.25 11.879 10.465
0.26 12.354 10.842
0.27 12.829 11.215
0.28 13.304 11.586
0.29 13.779 11.953
0.30 14.255 12.317
0.31 14.730 12.677
0.32 15.205 13.035
0.33 15.680 13.389
0.34 16.155 13.740
0.35 16.630 14.088
0.36 17.106 14.432
0.37 17.581 14.773
0.38 18.056 15.111
0.39 18.531 15.446
0.40 19.006 15.778
0.41 19.481 16.106
0.42 19.956 16.432
0.43 20.432 16.754
0.44 20.907 17.072
0.45 21.382 17.388
0.46 21.857 17.700
0.47 22.332 18.009
0.48 22.807 18.315
0.49 23.283 18.618
0.50 23.758 18.918
0.51 24.233 19.214
0.52 24.708 19.507
0.53 25.183 19.797
0.54 25.658 20.083
0.55 26.133 20.367
0.56 26.609 20.647
0.57 27.084 20.924
0.58 27.559 21.197
0.59 28.034 21.468
0.60 28.509 21.735
0.61 28.984 21.999
0.62 29.459 22.260
0.63 29.935 22.517
0.64 30.410 22.772
0.65 30.885 23.023
0.66 31.360 23.271
0.67 31.835 23.516
0.68 32.310 23.757
0.69 32.786 23.995
0.70 33.261 24.231
0.71 33.736 24.462
0.72 34.211 24.691
0.73 34.686 24.916
0.74 35.161 25.139
0.75 35.636 25.358
0.76 36.112 25.573
0.77 36.587 25.786
0.78 37.062 25.995
0.79 37.537 26.201
0.80 38.012 26.404
0.81 38.487 26.604
0.82 38.963 26.800
0.83 39.438 26.993
0.84 39.913 27.183
0.85 40.388 27.370
0.86 40.863 27.554
0.87 41.338 27.734
0.88 41.813 27.911
0.89 42.289 28.085
0.90 42.764 28.256
0.91 43.239 28.423
0.92 43.714 28.587
0.93 44.189 28.748
0.94 44.664 28.906
0.95 45.140 29.061
0.96 45.615 29.212
0.97 46.090 29.360
0.98 46.565 29.505
0.99 47.040 29.647
1.00 47.515 29.785
1.01 47.990 29.920
1.02 48.466 30.052
1.03 48.941 30.181
1.04 49.416 30.307
1.05 49.891 30.429
1.06 50.366 30.548
1.07 50.841 30.664
1.08 51.317 30.777
1.09 51.792 30.886
1.10 52.267 30.993
1.11 52.742 31.096
1.12 53.217 31.195
1.13 53.692 31.292
1.14 54.167 31.385
1.15 54.643 31.476
1.16 55.118 31.562
1.17 55.593 31.646
1.18 56.068 31.727
1.19 56.543 31.804
1.20 57.018 31.878
1.21 57.494 31.949
1.22 57.969 32.016
1.23 58.444 32.081
1.24 58.919 32.142
1.25 59.394 32.200
1.26 59.869 32.255
1.27 60.344 32.306
1.28 60.820 32.355
1.29 61.295 32.400
1.30 61.770 32.442
1.31 62.245 32.480
1.32 62.720 32.516
1.33 63.195 32.548
1.34 63.671 32.577
1.35 64.146 32.603
1.36 64.621 32.625
1.37 65.096 32.644
1.38 65.571 32.660
1.39 66.046 32.673
1.40 66.521 32.683
1.41 66.997 32.689
1.42 67.472 32.693
1.43 67.947 32.693
1.44 68.422 32.689
1.45 68.897 32.683
1.46 69.372 32.673
1.47 69.848 32.660
1.48 70.323 32.644
1.49 70.798 32.625
1.50 71.273 32.603
1.51 71.748 32.577
1.52 72.223 32.548
1.53 72.698 32.516
1.54 73.174 32.480
1.55 73.649 32.442
1.56 74.124 32.400
1.57 74.599 32.355
1.58 75.074 32.306
1.59 75.549 32.255
1.60 76.024 32.200
1.61 76.500 32.142
1.62 76.975 32.081
1.63 77.450 32.016
1.64 77.925 31.949
1.65 78.400 31.878
1.66 78.875 31.804
1.67 79.351 31.727
1.68 79.826 31.646
1.69 80.301 31.562
1.70 80.776 31.476
1.71 81.251 31.385
1.72 81.726 31.292
1.73 82.201 31.195
1.74 82.677 31.096
1.75 83.152 30.993
1.76 83.627 30.886
1.77 84.102 30.777
1.78 84.577 30.664
1.79 85.052 30.548
1.80 85.528 30.429
1.81 86.003 30.307
1.82 86.478 30.181
1.83 86.953 30.052
1.84 87.428 29.920
1.85 87.903 29.785
1.86 88.378 29.647
1.87 88.854 29.505
1.88 89.329 29.360
1.89 89.804 29.212
1.90 90.279 29.061
1.91 90.754 28.906
1.92 91.229 28.748
1.93 91.705 28.587
1.94 92.180 28.423
1.95 92.655 28.256
1.96 93.130 28.085
1.97 93.605 27.911
1.98 94.080 27.734
1.99 94.555 27.554
2.00 95.031 27.370
2.01 95.506 27.183
2.02 95.981 26.993
2.03 96.456 26.800
2.04 96.931 26.604
2.05 97.406 26.404
2.06 97.882 26.201
2.07 98.357 25.995
2.08 98.832 25.786
2.09 99.307 25.573
2.10 99.782 25.358
2.11 100.257 25.139
2.12 100.732 24.916
2.13 101.208 24.691
2.14 101.683 24.462
2.15 102.158 24.231
2.16 102.633 23.995
2.17 103.108 23.757
2.18 103.583 23.516
2.19 104.059 23.271
2.20 104.534 23.023
2.21 105.009 22.772
2.22 105.484 22.517
2.23 105.959 22.260
2.24 106.434 21.999
2.25 106.909 21.735
2.26 107.385 21.468
2.27 107.860 21.197
2.28 108.335 20.924
2.29 108.810 20.647
2.30 109.285 20.367
2.31 109.760 20.083
2.32 110.236 19.797
2.33 110.711 19.507
2.34 111.186 19.214
2.35 111.661 18.918
2.36 112.136 18.618
2.37 112.611 18.315
2.38 113.086 18.009
2.39 113.562 17.700
2.40 114.037 17.388
2.41 114.512 17.072
2.42 114.987 16.754
2.43 115.462 16.432
2.44 115.937 16.106
2.45 116.413 15.778
2.46 116.888 15.446
2.47 117.363 15.111
2.48 117.838 14.773
2.49 118.313 14.432
2.50 118.788 14.088
2.51 119.263 13.740
2.52 119.739 13.389
2.53 120.214 13.035
2.54 120.689 12.677
2.55 121.164 12.317
2.56 121.639 11.953
2.57 122.114 11.586
2.58 122.589 11.215
2.59 123.065 10.842
2.60 123.540 10.465
2.61 124.015 10.085
2.62 124.490 9.702
2.63 124.965 9.315
2.64 125.440 8.926
2.65 125.916 8.533
2.66 126.391 8.137
2.67 126.866 7.738
2.68 127.341 7.335
2.69 127.816 6.929
2.70 128.291 6.521
2.71 128.766 6.108
2.72 129.242 5.693
2.73 129.717 5.274
2.74 130.192 4.853
2.75 130.667 4.428
2.76 131.142 3.999
2.77 131.617 3.568
2.78 132.093 3.133
2.79 132.568 2.695
2.80 133.043 2.254
2.81 133.518 1.810
2.82 133.993 1.362
2.83 134.468 0.911
2.84 134.943 0.457
2.85 135.419 0.000

 

Mark McVey

"The work of science is to substitute facts for appearances and demonstrations for impressions." -John Ruskin
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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/08 at 11:43am

I have the drag case worked out and will post later.  I have in spreadsheet so if anybody want to double check the calculations, improve on them, .... my feelings will not be hurt. 

Since this is a safety issue, it would be proper and wise to have the formulas checked out as we do not want a safety incident anywhere let alone at one of the big games.

I make no claims to accuracy and if the formulas are used to make safety judgement, you use them at your own risk.... in other words I do not want to be sued because I tried working on a math problem in an area where I have NO formal training!

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/08 at 6:54pm

If I got the formulas correct, the following graph is the path assuming

  • formulas:  http://www.grc.nasa.gov/WWW/K-12/airplane/flteqs.html
  • Release angle of 44 degrees which appears to be close to optimal.
  • Release Velocity of 66.5 feet/sec -- Top Olympic hammer throwers release velocity is 70 feet/second.  This facts makes me wonder if the formula and/or results are valid as I am not sure whether a top SCottish hammer thrower can closely match the releas velocity of top T&F wire hammer throwers.  However, the value of 67 feet/sec does produce a throw around 135 ft.
  • Drag Coefficient: I set this to 0.75  Complete guess work.  Wire hammer drag coefficient is 0.70 (from a biomechinical article). Sphere drag Coefficient is 0.47.  Long cylindar's DC is 0.82 (http://en.wikipedia.org/wiki/Drag_coefficient)
  • Cross Section: Used in drag calculation and is that of a circle that is 4.25" diameter.  Probably okay if the hammer flys head first.

 

t x y
0.00 0.00 0.000
0.01 0.48 0.460
0.02 0.96 0.917
0.03 1.43 1.371
0.04 1.91 1.822
0.05 2.39 2.269
0.06 2.87 2.713
0.07 3.35 3.154
0.08 3.83 3.591
0.09 4.30 4.026
0.10 4.78 4.457
0.11 5.26 4.884
0.12 5.74 5.309
0.13 6.22 5.730
0.14 6.69 6.148
0.15 7.17 6.563
0.16 7.65 6.975
0.17 8.13 7.383
0.18 8.60 7.788
0.19 9.08 8.190
0.20 9.56 8.588
0.21 10.04 8.983
0.22 10.51 9.376
0.23 10.99 9.764
0.24 11.47 10.150
0.25 11.95 10.532
0.26 12.42 10.911
0.27 12.90 11.287
0.28 13.38 11.660
0.29 13.86 12.029
0.30 14.33 12.395
0.31 14.81 12.758
0.32 15.29 13.117
0.33 15.76 13.474
0.34 16.24 13.827
0.35 16.72 14.177
0.36 17.20 14.523
0.37 17.67 14.867
0.38 18.15 15.207
0.39 18.63 15.544
0.40 19.10 15.877
0.41 19.58 16.208
0.42 20.06 16.535
0.43 20.53 16.859
0.44 21.01 17.180
0.45 21.49 17.497
0.46 21.96 17.811
0.47 22.44 18.122
0.48 22.92 18.430
0.49 23.39 18.735
0.50 23.87 19.036
0.51 24.34 19.334
0.52 24.82 19.629
0.53 25.30 19.920
0.54 25.77 20.209
0.55 26.25 20.494
0.56 26.73 20.776
0.57 27.20 21.054
0.58 27.68 21.330
0.59 28.15 21.602
0.60 28.63 21.871
0.61 29.11 22.137
0.62 29.58 22.399
0.63 30.06 22.658
0.64 30.53 22.914
0.65 31.01 23.167
0.66 31.49 23.417
0.67 31.96 23.663
0.68 32.44 23.906
0.69 32.91 24.146
0.70 33.39 24.383
0.71 33.86 24.616
0.72 34.34 24.846
0.73 34.81 25.073
0.74 35.29 25.297
0.75 35.77 25.517
0.76 36.24 25.735
0.77 36.72 25.949
0.78 37.19 26.159
0.79 37.67 26.367
0.80 38.14 26.571
0.81 38.62 26.772
0.82 39.09 26.970
0.83 39.57 27.165
0.84 40.04 27.356
0.85 40.52 27.545
0.86 40.99 27.730
0.87 41.47 27.911
0.88 41.94 28.090
0.89 42.42 28.265
0.90 42.89 28.437
0.91 43.37 28.606
0.92 43.84 28.772
0.93 44.32 28.934
0.94 44.79 29.093
0.95 45.27 29.249
0.96 45.74 29.402
0.97 46.21 29.552
0.98 46.69 29.698
0.99 47.16 29.841
1.00 47.64 29.981
1.01 48.11 30.117
1.02 48.59 30.251
1.03 49.06 30.381
1.04 49.54 30.508
1.05 50.01 30.632
1.06 50.48 30.752
1.07 50.96 30.870
1.08 51.43 30.984
1.09 51.91 31.094
1.10 52.38 31.202
1.11 52.85 31.306
1.12 53.33 31.408
1.13 53.80 31.506
1.14 54.28 31.600
1.15 54.75 31.692
1.16 55.22 31.780
1.17 55.70 31.865
1.18 56.17 31.947
1.19 56.64 32.026
1.20 57.12 32.101
1.21 57.59 32.173
1.22 58.07 32.242
1.23 58.54 32.308
1.24 59.01 32.370
1.25 59.49 32.430
1.26 59.96 32.486
1.27 60.43 32.539
1.28 60.91 32.588
1.29 61.38 32.635
1.30 61.85 32.678
1.31 62.33 32.718
1.32 62.80 32.755
1.33 63.27 32.788
1.34 63.75 32.818
1.35 64.22 32.846
1.36 64.69 32.869
1.37 65.16 32.890
1.38 65.64 32.908
1.39 66.11 32.922
1.40 66.58 32.933
1.41 67.06 32.941
1.42 67.53 32.945
1.43 68.00 32.946
1.44 68.47 32.945
1.45 68.95 32.939
1.46 69.42 32.931
1.47 69.89 32.920
1.48 70.36 32.905
1.49 70.84 32.887
1.50 71.31 32.866
1.51 71.78 32.841
1.52 72.25 32.814
1.53 72.73 32.783
1.54 73.20 32.749
1.55 73.67 32.711
1.56 74.14 32.671
1.57 74.62 32.627
1.58 75.09 32.580
1.59 75.56 32.530
1.60 76.03 32.476
1.61 76.50 32.420
1.62 76.98 32.360
1.63 77.45 32.297
1.64 77.92 32.231
1.65 78.39 32.161
1.66 78.86 32.088
1.67 79.34 32.012
1.68 79.81 31.933
1.69 80.28 31.851
1.70 80.75 31.765
1.71 81.22 31.676
1.72 81.69 31.584
1.73 82.17 31.489
1.74 82.64 31.391
1.75 83.11 31.289
1.76 83.58 31.184
1.77 84.05 31.076
1.78 84.52 30.964
1.79 85.00 30.850
1.80 85.47 30.732
1.81 85.94 30.611
1.82 86.41 30.487
1.83 86.88 30.359
1.84 87.35 30.229
1.85 87.82 30.095
1.86 88.29 29.958
1.87 88.76 29.817
1.88 89.24 29.674
1.89 89.71 29.527
1.90 90.18 29.377
1.91 90.65 29.224
1.92 91.12 29.067
1.93 91.59 28.908
1.94 92.06 28.745
1.95 92.53 28.579
1.96 93.00 28.409
1.97 93.47 28.237
1.98 93.94 28.061
1.99 94.41 27.882
2.00 94.88 27.700
2.01 95.36 27.514
2.02 95.83 27.326
2.03 96.30 27.134
2.04 96.77 26.939
2.05 97.24 26.740
2.06 97.71 26.539
2.07 98.18 26.334
2.08 98.65 26.126
2.09 99.12 25.915
2.10 99.59 25.701
2.11 100.06 25.483
2.12 100.53 25.262
2.13 101.00 25.038
2.14 101.47 24.811
2.15 101.94 24.580
2.16 102.41 24.347
2.17 102.88 24.110
2.18 103.35 23.869
2.19 103.82 23.626
2.20 104.29 23.379
2.21 104.76 23.130
2.22 105.23 22.877
2.23 105.70 22.620
2.24 106.17 22.361
2.25 106.64 22.098
2.26 107.11 21.832
2.27 107.57 21.563
2.28 108.04 21.291
2.29 108.51 21.015
2.30 108.98 20.736
2.31 109.45 20.454
2.32 109.92 20.169
2.33 110.39 19.881
2.34 110.86 19.589
2.35 111.33 19.294
2.36 111.80 18.996
2.37 112.27 18.695
2.38 112.74 18.390
2.39 113.21 18.082
2.40 113.68 17.771
2.41 114.14 17.457
2.42 114.61 17.140
2.43 115.08 16.819
2.44 115.55 16.495
2.45 116.02 16.168
2.46 116.49 15.838
2.47 116.96 15.504
2.48 117.43 15.167
2.49 117.89 14.827
2.50 118.36 14.484
2.51 118.83 14.138
2.52 119.30 13.788
2.53 119.77 13.435
2.54 120.24 13.079
2.55 120.71 12.720
2.56 121.17 12.357
2.57 121.64 11.991
2.58 122.11 11.622
2.59 122.58 11.250
2.60 123.05 10.875
2.61 123.52 10.496
2.62 123.98 10.114
2.63 124.45 9.729
2.64 124.92 9.341
2.65 125.39 8.950
2.66 125.86 8.555
2.67 126.32 8.157
2.68 126.79 7.756
2.69 127.26 7.351
2.70 127.73 6.944
2.71 128.20 6.533
2.72 128.66 6.119
2.73 129.13 5.702
2.74 129.60 5.281
2.75 130.07 4.857
2.76 130.53 4.430
2.77 131.00 4.000
2.78 131.47 3.567
2.79 131.94 3.130
2.80 132.40 2.691
2.81 132.87 2.248
2.82 133.34 1.801
2.83 133.81 1.352
2.84 134.27 0.899
2.85 134.74 0.443
2.86 134.74 0.000

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/05/08 at 7:03pm

Two graphs the first shows the difference in distance when factoring drag and holding all else the same.

A more interesting result which maybe more helpful as the no drag model is simplier to work with.  The plot of two paths in which the resulting distances are about 135' but one path consider drag, and the other does not.  They paths lie almost on top of each other.

 

 

 

 

 

 

 

 

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/06/08 at 4:08am

last few caeveats:

I did not consider the release height, which will slightly change the distance traveled as well as the trajectory.

If my spreadsheet is correct, drag does not have a great impact on the path traveled and thus should not have a great impact on the problem you want to solve.  The formulas at:

http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

are good and with a spreadsheet others can plug and chug values in to answer some questions.

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote WALLY.OLECIK Quote  Post ReplyReply Direct Link To This Post Posted: 11/06/08 at 4:43pm
Wayne Hill and McSanta -

Thanks so much!!  Looks like l've got some changes to make to the lay-out of our field!
16lb-hammer(at)sshga.org

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Post Options Post Options   Thanks (0) Thanks(0)   Quote C. Smith Quote  Post ReplyReply Direct Link To This Post Posted: 11/25/08 at 10:47am
Those graphs are nice and all, but i'm telling you guys i have been 35'+ high with a 22lb hammer and it still landed at 101+.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/25/08 at 11:54am

Not to fear, in the results sent to Wally, I included a "limiting" or worse case scenario.  

In this scenario, I assumed the thrower could not produce a release speed greater than that obtain on a wire-hammer by Olympic level thrower.  (I found this value in a biomechanical journal and that was70 ft per second.) 

I am not an expert on sports medicine or bio mechanics but I believe this is a solid limiting assumption as the wire hammer is shorter in length and thrown with a movement that should generate more speed than the Scottish Hammer. 

Playing around with the launch angle, it appears that a launch angle of just under 60 degrees would produce the highest hammer throw (over 60 feet) and land about 135 out.  At 100ft out, the hammer is 47' off the ground!  

If one assumed no drag, it is a simple mathematical solve to find the release angle that would produce the highest path at 100 ft out given a release speed.  I did not get around to solving that for him. 

Never the less, Wally was given the limiting case which gives him a height of 47' to worry about.  By his comments, I assume he is making approrpiate adjustments.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/25/08 at 11:56am

From a practical point of view, how tall would a thrower have to be to launch the Scottish hammer at a 60 degree angle?  


Sine of 60 degree angle time 50 inches = 43.3 inches ... the height off the ground of the end of the hammer handle when it is leaned on a 60 degree angle....

I think the thrower would have to be rather tall to launch the Scottish hammer on a 60 degree angle!!!

Same calculation but a 45 degree angle, and the end of the hammer handle is just over 35 inches off the ground.

So maybe 6'6 to 6'8" tall?

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Post Options Post Options   Thanks (0) Thanks(0)   Quote AncientOne Quote  Post ReplyReply Direct Link To This Post Posted: 11/26/08 at 5:22am
Hey-

By the way, as I recall Craig Smith hit a ceiling fan mounted on steel cross beam in the Coliseum on the Illinois State Fairgrounds during the Shamrock Games. The cross beam is at 40' above the ground surface and the fan is a few feet lower. He spun the blades without breaking any and still threw the heavy hammer to 104'.

-K
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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/26/08 at 6:49am

Release Angle: 52 degree 

Speed of hammer head upon release 57.5 ft/sec (82.5% of Oly level wire hammer thrower who is throwing Wire hammer is shorter in length and lighter implement)

Drag coefficient = 0.72
(wire hammer is 0.7, sphere is .47, long cylinder is 0.84 )

Hammer head's diameter is 4.5" 
(need for cross section to calc drag reduction)

These values yield: 

Height just over 38' at just over 50' horizontal distance from launch point.

Distance just over 104'

-------------------------------

I am not a physicist or an engineer... However, the input (angle and velocity) to reproduce Craig's throw seems reasonable ... perhaps a bit steep on release angle but I don't never know.

Given the coliseum earth (no turf to dig under, just well packed soil and hourse droppings?), how hammer boots don't always hold (excpecially later in the day ...but Super A's thrower earlier), early season form, .... maybe the angle is reasonable as the athletes maynot be as aggressive with the hammer throw in other conditions. I really don't know and the above maybe a plausible explanation of the release angle.

---------------------

It is always cool watching the Shammies in the coliseum.

 

Mark McVey

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Post Options Post Options   Thanks (0) Thanks(0)   Quote McSanta Quote  Post ReplyReply Direct Link To This Post Posted: 11/26/08 at 7:09am

In case anybody is interested:

Some hammer flight paths that where generated for Wally's problem, the projected path of the highest hammer (at 100' out), the possible path for the world record throw, and a possible path of Craig Smith's imfamous or famous heavy hammer throw that hit the ceiling fan at the Shamrock Games.

 

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Post Options Post Options   Thanks (0) Thanks(0)   Quote WALLY.OLECIK Quote  Post ReplyReply Direct Link To This Post Posted: 1/05/09 at 2:42pm
Once again, thanks go out to Wayne Hill and McSanta for all of the assistance that
they've given me on my safety issues.  l've decided to restrict the hammer throws
to a very narrow impact sector (40 degrees) to impress upon the throwers the
importance of keeping the hammer away from the spectator seating area. 
This is the size of sector that will be used at the Master's World and slightly wider
that used at many Games in Scotland.  This won't change the length of the field on
that side but if an athlete is going to throw that far, it seems that they will also be
able to control the direction of their throws.
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