Calculate Axle Load Using FBD:
The axle loads of a vehicle can be calculated using a schematic drawing and the vehicle data. An FBD (Free Body Diagram) allows you to draw a vehicle with the relevant forces (see image below). The conditions for an FBD are that the road surface should not be drawn. Even if the vehicle is on a hill, it should not be drawn inclined, but a horizontal force with a direction should be drawn in the FBD.
The advantage of working with an FBD is that unnecessary elements are omitted. When, for example, calculating the internal moments or axle load of a trailer, it is useful to only draw the trailer instead of a car with a trailer. By only drawing what is necessary, you avoid making mistakes (by including too many horizontal/vertical forces in the calculation that do not belong there).
First, the weight must be calculated using the gravitational acceleration acting on the vehicle. Gravity depends on the location on Earth where the vehicle is located. In the Netherlands, the gravitational acceleration is 9.81m/s.
The vehicle mass must be multiplied by gravity. This gives: 1500 x 9.81 = 14,715N (The unit of force is Newton). It should be noted here that gravitational acceleration is sometimes also called gravitational constant or free-fall acceleration. The number 9.81 is sometimes rounded to 9.8 or very roughly to 10. While this makes mental calculations easier (1500 / 10 is easier to calculate in your head than 1500/ 9.81), the final answer is definitely not precise. Therefore, always apply 9.81m/s unless stated otherwise in, for example, an exam question.
The total force with which the vehicle is pressed on the road surface is therefore 14,715 Newton. This force is distributed over both axles of the car.
The axle load at the front is often higher because that’s where the engine is located. This is visible in the image by the center of gravity, which is located towards the front from the middle. The center of gravity is an imaginary pivot point. If this center of gravity were exactly in the middle, the axle load on both axles would be equal (vehicle mass divided by 2). Since the distances of the wheels, the location of the center of gravity, and the total vehicle mass are known, the axle loads at the front and rear can be calculated.
Vehicle mass: 1500 kg
Weight: 14715 N
Height road surface – pivot point: 60 cm
Distance F1 – pivot point: 115 cm
Distance pivot point – F2: 160 cm
Distance F1 – F2: 115 + 160= 275 cm (this is the wheelbase)
Calculate Rear Axle Load (F2):
14715 x 1.15 – F2 x 2.75 = 0
16922 – F2 x 2.75 = 0
F2 = 16922 / 2.75
F2 = 6154 N
The calculation is elaborated below:
- To calculate F1 and F2, one must be calculated first. We choose to calculate F2 first.
We make the pivot point at F1. Everything clockwise is positive and everything counterclockwise is negative. That means the forces pointing down are positive, and the force F2 pointing up is negative. We fill in the first part of the formula.
14715 x 1.15 – F2 x 2.75 = 0
(This last 0 is standard to fill in, because further in the calculation, the numbers on the left and right of the ” = ” sign are swapped) - Force x arm: The weight of 14715 is multiplied by the distance of 1.15:
14715 x 1.15 = 16922 - Now we fill this again in the formula:
16922 – F2 x 2.75 = 0 - Move the 16922 to the other side where the 0 is:
F2 x 2.75 = 16922 - Divide both sides by 2.75 to remove it from the left of the = sign:
F2 = 16922 / 2.75 - That results in:
F2 = 6154 N.
Difference Between Weight and Mass:
Remember that weight is not the same as mass. The weight of F2 in the previous calculation is 6154 Newton. Mass is always in kilograms. It must therefore always be divided by the gravitational acceleration of 9.81. (6154 / 9.81 = 627.3 kg) Consider the vehicle’s curb weight that is mentioned on the registration certificate. That is also always in kg. To make the above explanation clear; In space, there is no gravity. Everything floats there, regardless of how heavy it is. However, everything does indeed have weight; when you throw a carton of milk against something, or a stone, it will have a different impact. The carton of milk will not damage anything when it hits the wall, but the stone will cause damage. This is because the force with which the object comes to a stop is higher for the stone than for the carton of milk. This proves that weight is also present in space and is important, but mass is not. Mass arises due to the Earth’s gravitational pull. Therefore, the weight of the car is not 1200 kg, but the mass is 1200 kg. Many mistakes are often made with this.
Calculate Front Axle Load (F1):
When the total weight and 1 axle load are known, the 2nd axle load can be easily calculated by subtracting these two from each other:
Total weight – F2 = F1:
14715 – 6154 = 8561N.
F1 can of course also be calculated separately. It is nearly the same as the first calculation:
14715 x 1.6 – F1 x 2.75 = 0
23544 – F1 x 2.75 = 0
F1 = 23544 / 2.75
F1 = 8561N
The force the front wheel exerts on the road surface is 8561N and the rear wheel 6154N. Combined, this totals 14715N. Therefore, the total vehicle mass is 14715 / 9.81 = 1500kg.
Calculate Tongue Load:
In the same way that the axle loads of the car were calculated in the previous sections, the tongue load on the car’s hitch can also be determined. Moment is force x arm. This means that the longer the arm, the greater the moment becomes. The rear axle load depends on the distance between F2 and F3, and the tongue load depends on the distance between F3 and F4. And precisely the force on ‘the pivot point’, or the hitch ball, must be calculated.
The car weighs 1500kg, and the trailer 300kg. We first convert these again to Newton by multiplying by gravitational acceleration:
1500 x 9.81 = 14715N
300 x 9.81 = 2943N
To calculate the tongue load, it is easier to first only draw the trailer. The car itself is not important in the calculation.
The tongue load is indicated with F3 and the force with which the tire presses on the road surface as F5.
F3 becomes the pivot point, and we will calculate the force F5. The center of gravity is a downward force, so positive. The force acting on F5 is a force upward, so it is negative (hence a minus sign is placed in front). The weight of the trailer is 4000N.
Calculate the force F5:
4000 x 1.2 – F5 x 1.4 = 0
4800 – F5 x 1.4 = 0
F5 = 4800 / 1.4
F5 = 3429N
Calculate the tongue load (F3):
4000 – 3429 = 571N
571 / 9.81 = 58.2kg
The tongue load with this trailer is 58.2kg.
If the center of gravity moves backward, the tongue load becomes smaller. To gain insight and practice the calculations, it is helpful to increase and decrease the distance between F3 and F4 and thus between F4 and F5 and redo the calculation.
Calculate the Influence of Tongue Load on the Rear Axle:
Since the tongue load is now known, it can be calculated what effect this has on the rear axle. The weight cannot be simply added up, as the distance between the rear axle and the hitch ball is of great significance (force x arm). We use the same image of the car with the trailer again.
In the previous calculation, it became known that the tongue load (F3) amounts to 571N. F2 was also known, which was 6154N. The forces cannot be added together, as the distance between the rear wheel and the hitch ball’s head still functions as an arm. We remake the entire formula, as at the very beginning of this page. In this formula, 571 x 3.65 is also added (the force at F3 with the distance from F1 to F3 added up).
14715 x 1.15 + 571 x 3.65 – F2 x 2.75 = 0
19006 – F2 x 2.75 = 0
F2 = 19006 / 2.75
F2 = 6911N = 691kg.
This means that a weight of 691kg rests on the rear axle.