High School Maths 07/06

Some time ago I came across another 60’s rule which makes load calculations simple.

The force required to move a weight up a slope with an angle B is derived by the formula:-

Fire up the trustee computer and behold you can calculate the following for a loaded up Pajero

The problem with this formula is it requires a computer or a scientific calculator and generally neither of which we take away on the weekend

Now there is a very simple 60’s formula which gives a sufficiently accurate result and requires nothing more then a mobile telephone for the calculator and a half empty wine bottle.

Physics		60’s Rule
2400 * Sin(15)	621 kg	2400 / 60 * 15 degrees	600 kg
2400 * Sin(25)	1014 kg	2400 / 60 * 25 degrees	1000 kg
2400 * Sin(30)	1200 kg	2400 / 60 * 30 degrees	1200 kg
2400 * Sin(40)	1543 kg	2400 / 60 * 40 degrees	1600 kg
2400 * Sin(50)	1838 kg	2400 / 60 * 50 degrees	2000 kg

It starts to get a bit out at the high numbers but would only cause to us to err on the side of caution so I think it is acceptable.

Now all you need to know is how far your eyes are from the ground so when you hold up your half empty wine bottle (no, we don’t drink and drive) as a level you can guess the distance to get the angle.

The angle of the slope requires careful consideration as the world is neither flat nor comprised of even slopes. For example a well known rock shelf at Brooklyn is a combination of individual slopes of 15 and 45 and 70 degrees each of which need to be considered in the overall exercise. Next month we will look at the condition of the surface and its effect on the load.

The foregoing was calculated by an accountant and not an engineer. Accordingly it is offered for comment and discussion but no warranty as to the reliability or accuracy of the information is given or implied.

The earth isn’t flat and the surface also changes to add to our amusement. Sometimes it is bitumen, sometimes grass, and for 4WDers usually dirt but also often sand or mud. Ask anyone who has been bogged and they will soon tell you it’s a lot harder to move a vehicle if it is bogged in mud than it is to move one on dry ground. So we need to make some allowance for the condition of the surface in our calculations of the load.

The following I believe is commonly used by a large organisation which specialises in drab green or camouflage trucks around Australia. The process is to add to the calculation from last month a fraction of the total weight to be moved.

Surface	Bitumen	Grass	Gravel	Sand	Mud
Factor	1/25th	1/7th	1/5th	1/4th	1/2
Weight 2400 kg	100 kg	345 kg	480 kg	600 kg	1200 kg

By combining the table from last month and this one we get the following calculation of the potential load:-

	Bitumen	Grass	Gravel	Sand	Mud
15 degrees	721 kg	966 kg	1101 kg	1221 kg	1821 kg
25 degrees	1014 kg	1359 kg	1494 kg	1614 kg	2214 kg
30 degrees	1300 kg	1545 kg	1680 kg	1800 kg	2400 kg
40 degrees	1643 kg	1888 kg	2023 kg	2143 kg	2743 kg
50 degrees	1938 kg	2183 kg	2318 kg	2438 kg	3038 kg

These are basic numbers and the practice of adding 10% as a safety margin has considerable merit. All of the calculations in this exercise have been done in kilograms as the winch data normally refers to kgs per layer on the drum. The maximum load for the last two layers on my 4000kg winch is 3115kg and 3333kg. Both of which are below the 10% margin applied to the Mud column at 50degrees

A panel beater has also suggested all loadings should be applied down the centre line of an NM/NP vehicle level with the floor pan/“chassis structure”. He suggests the vehicle may suffer “chassis” distortion when loadings as low as 1500kgs are either not down the centre line or one wheel causes resistance to recovery. His suggestion was to watch the gaps around doors if in doubt but I suspect by the time the gap visibly changes it is too late. It begs the question should we always use equaliser straps with NM/NP vehicles if the recovery point is to one side?

All the calculations have been based on a stationery recovery vehicle. The dynamics change dramatically if the recovery vehicle is moving such as the basic snatch strap recovery.

Out on your weekend away you come across a Nissan Patrol loaded to the hilt GVM 3040kgs with a 1200kg camper on the back stuck half way up a muddy hill with a slope of 30degrees. What is the potential load?? First correct answer at the meeting wins the prize. Just to get in ahead of some, no you cannot leave it there!