The RTI With Or Without A Ramp
By Doug Chartier

The RTI With or Without a Ramp

by Doug Chartier

 **** Corrections for the below article**** article**** article****

There are 2 corrections to Doug’s RTI article last month. FIRST CORRECTION:  Next to last paragraph, next to last line:  Was, "corresponds to... sine .2643..."  SHOULD read, "sine .2653" - a typo.  SECOND CORRECTION:  Last paragraph, 3rd line from bottom, and this throws the answer off considerably.  Formula for side c is a/sine A.  That is correct.  I used 98, the wheelbase, instead of 26, the actual length of side a, so the calculation is: 26/.3420 = 76.02 - Your vehicle will drive 76" up a 20-degree ramp.  To figure the RTI the formula is "travel up ramp divided by wheel base times 1000."  76/98 = .7755 times 1000 = 775.5.   Your RTI would be 775 on a 20-degree ramp.  

**** We do our best but sometimes the printer gets it before we done!!!****

It really isn't very difficult to determine your Ramp Travel Index with a ramp or WITHOUT a ramp. All you need to do is get one front wheel off the ground to the point that another wheel just leaves the ground. You can use a ramp, big pile of dirt, a jack, winch or a strong neighbor or family member.

 OBJECTIVE: To determine the RTI (Ramp Travel Index) of your vehicle on any degree of RTI Ramp.

 TOOLS NEEDED: Tape measure, a sine table or a calculator that will calculate sines, angles etc. Calculators cost less than $20.

 MEASUREMENTS: Wheelbase of vehicle from the center of the front axle to the center of the rear axle and the distance from bottom of tire raised off the ground to the ground.  

Figure 1 below:

 1) A, B & C are angles of a right triangle

 2) a, b & c are the sides opposite the angles

 3) A is the “Ramp Angle

 4) c is the hypotenuse of the right triangle

 

Don't leave me now. This is trigonometry, but it is really pretty simple and also fun. Only a couple of formulas involved.

 Having the value of any TWO of the above – A, B, C or a, b, c will allow you to calculate ALL the other values.  The only thing you need is the sine of the angles.  Sines can be computed on a hand calculator that does Trig formulas or can be gotten from a sine table.  A brief sine table is provided at the end of this article.

 c = a / sine A (length of c)

 The formula for determining the Ramp Travel Index is:

 Travel up ramp divided by wheel base times 1000

 There are two reasons for using a ramp. The first is because it is easier to drive it up than to lift it up. The second is that angle A of a fabricated ramp is a known factor. If you are able to determine the wheel lift in inches and know an angle or the length of another side, you can calculate the RTI on any degree ramp. If you don't have a ramp, devise a method of raising a wheel and taking the measurement. All the rest is done on paper.

 We are going to calculate two different things. First will be the angle of the ramp upon which your vehicle would have an RTI of exactly 1000. The second is the method of determining the RTI on a ramp of ANY angle based on the figures derived from your measurements - wheel height and wheelbase.  Figure 2:

  All measurements are made straight up and down from the center of each axle. As you can see the back wheel appears to be a slight distance up the ramp. It is. The axle needs to be directly over the end of the ramp.

We are going to assume now that you have not used a ramp. The front wheel has been raised with a jack. Measure from the bottom of the front tire at its center to the ground.

For this example we will assume the wheelbase is 98 inches, and the lift of the front wheel is 26 inches.  Note that the wheelbase is the same measure as side c in figure 1, the lift, 26 inches, is the same as side a in figure 1.  Therefore we know TWO of the values of the triangle.  With two values we can calculate all the values.

 From this data we want to determine two things. The ramp upon which the vehicle will ramp a perfect 1000, and the RTI of any ramp of a specified degree. We need the sine of angle A so that we can check a sine table or use our calculator to calculate the angle.

The sine of an angle is the length of the side opposite that angle divided by the length of the hypotenuse. 26 inches (length of side

a) divided by 98 inches (length of c) is .2653. The angle that corresponds to the sine .2643 is 15 degrees, 23 minutes (60 minutes in a degree, so 23 minutes is a bit over 1/3 of a degree).

 Now, how about using our known information to determine the RTI of a 20 degree ramp. Again we have two pieces of data, the lift or side a - 26 inches - and angle A. We just assigned it, 20 degrees. We do not know c because we do not know where the beginning of the ramp will be in relation to the wheelbase on this 20 degree ramp. It will be calculated based on known information. We need the length of side c so that we can divide it into the length of a for the RTI calculation.  The formula for side c is: a / sine A.  The sine of 20 degrees is .3420.  98/.3420 is 58.47 or 58.5 inches.  Your vehicle would drive 58.5 inches up a 20 degree ramp.  Do the RTI math and find that is an RTI of 596 on a 20 degree ramp.

12- .2079          17- .2924            22- .3746            27- .4540  
13- .2250          18- .3090            23- .3907            28- .4695  
14- .2419          19- .3256            24- .4067            29- .4848  
15- .2588          20- .3420            25- .4226            30- .5000  
16- .2756          21- .3584            26- .4384            31- .5150