# Total Gym Math

**12/12/08**

I recently ordered and put together a Total Gym XLS.

Setting up the Total Gym XLS got me thinking about the mathematics behind the Total Gym, because it is essentially a right triangle.

The approximate 90" length of the base comes from the manual, as do the angles. Notice that the height of the triangle, h_{α}, depends on the angle α. Solving for h_{α} gives h_{α} = 90 * tan(α). Evaluating this for the α's for levels 1-6 on the Total Gym gives

Level | α | h_{α} (in.) |
---|---|---|

6 | 26.0 | 43.89 |

5 | 22.3 | 36.91 |

4 | 18.4 | 29.93 |

3 | 14.4 | 23.10 |

2 | 10.2 | 16.19 |

1 | 6.0 | 9.45 |

This minor mathematical exercise got me thinking about the resistances shown in the manual. They show resistances for levels 1-6 for bodyweights ranging from 50-250 lbs in 10 lb increments. I'd like to have the formula that created these numbers, because if I weigh 204.7 lbs, for example, the resistances don't apply exactly as shown.

If I weigh w lbs, the resistance is approximately w * sin(α). However, when I used this to calculate, I noticed that my numbers were a little off from what the Total Gym literature shows. When I did the formula weight * sin(α), for weight = 200 lbs, I got numbers very close to what the chart shows for 180 lbs. Therefore, I added 23 lbs to the weight, which gets me very close if not exact. So if I want the result for a bodyweight of 200 lbs, I use the formula with 223 lbs. The weight of 23 lbs is probably the constant additional weight of the sled and accessories.

### Total Gym Randomizer

Using my Weighted Exercise idea, I've created a randomizer program for the Total Gym. The Total Gym Randomizer is available here. Upon opening the spreadsheet and entering in your bodyweight and any additional weight you may have on the Total Gym weight bar, it creates a workout and shows you the levels you are on for various exercises, the calculated resistances being used, the accessory needed, and the number of the card in the Total Gym deck corresponding to the exercise or the source if the exercise came from elsewhere. An example is:

In addition to the variety of exercises one can do on the Total Gym, I'm finding the Total Gym useful because it has the benefits of strength training machines such as safety and quick transitions between exercises, as well as the benefits of freeweights such as having to work to stabilize more. Since the weight used is primarily your bodyweight, the Total Gym automatically gets you conscious of your bodyweight. Additionally, Dr. Ben Bocchicchio, the person who suggested slow style training to Ken Hutchins of SuperSlow, promotes training on the Total Gym. To quote Fred Hahn of SlowBurn

Sounds good to me!"Dr. Ben who invented SMaRT training is a friend and says that he was amazed by the results the TG produced in one of his studies. He said it shocked him. It made him think that the equipment used makes little difference ITO outcomes so long as effort and weight load is sufficient."

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