Calculating Axle Loads for a Firefighter Vehicle: A Statics Problem

[MasterG]

Hi, my name is Goran and I have a physics/mechanics problem.
I'm a 3D artist and I do 3D CAD or non CAD models for a company I work at. New job I got is basically a engineer because I'm about to get my mechanical engineering degree, but it has been a long time I actually calculated something so I need help and it is really simple for someone that knows what to do.

I've read the forum and found some solutions and calculations for my problem but since my English is not the best in the world I ask for your help and consideration.

SO here is the problem.

We built a firefighter vehicle from IVECO 80E18D chassis. Okay, so I constructed the frame that holds the box at the back of the chassis, tank with 1500 L capacity and all the shelves, boxes, lights and stuff a firefighter needs to have.

The metal structure= 300 kg + 100 kg (all the sheet metal)
The tank= 1500 kg (of water) + 20 kg (weight of tank)
The crew is 3 (front) + 4 (back) = 7 * 75kg = 525 kg
The pump = 150 kg

Now I need to calculate the axle loads and see if it is within the manufacturers permissions. We actually went to measure it on scale AFTER MODIFYING IT (adding the structure, tank, pump and all that so finished truck) and the results are like this:

WITHOUT ANY FLUID IN TANK (without crew)
front axle 2690 kg
rear axle 2850 kg
WITH FLUID IN TANK (without crew)
front axle 2910 kg
rear axle 4160 kg

So, since the manufacturer specifies the front axle limit is 3600 kg and the rear axle limit is 5800 kg we should be fine, right? It basically a statics problem, but like I said, it has been a long time since I used mechanics calculations.

http://tinypic.com/r/hv71wh/8

 

[Baluncore]

What is the question ?
Do you want to know how to calculate the centres of mass being applied to the two axles ?
You need the x position and mass of each component you are adding to the structure.

 

[MasterG]

the question is HOW can I calculate the centre of mass, and axle load?

I have IVECO official documentation sheet, link is in the first post so you an check that
so KERB weight is
2655kg FRONT AXLE
1045kg REAR AXLE

major equipment added on:
construction (black on picture) = 350kg
water tank (blue) = 1500L + 20 kg (actual tank) = 1570kg
water pump (red) = 150kg

center of gravity for each of this parts is on 50% (middle) of their horizontal line. And I added the "x" distance from the front axle for each component. See the picture http://tinypic.com/r/5uofmu/8But when we added all the construction, water tank, water pump we went to scale it and the results are:
WITHOUT ANY FLUID IN TANK (without crew)
front axle 2690 kg
rear axle 2850 kg
WITH FLUID IN TANK (without crew)
front axle 2910 kg
rear axle 4160 kgSo I need to calculate the center of gravity, and axle loads, but how?
I understand I need to use statics over axles, but like I said there is no internet material on this on my language, and my English is not that good to understand kerb, unladen, cerb, tare weight and all that.

 

[Baluncore]

Assume the empty weight of the tank is 70 kg, not 20kg.
The wheelbase is; a = 4185. mm
Measure position, x, of centroids from front axle, positive towards the rear axle.
A centroid applies it's total mass, m, in kg, to both axles in proportion to the position x along the wheelbase.
The two components are;
rear axle = m * x / a
front axle = m * ( a - x ) / a
Notice that these components will always total m.
If a centroid is outside the wheelbase it can generate a negative component.

The input data is;
Item, mass m, position x
"Front tare", 2655 kg, 0 mm
"Rear tare ", 1045 kg, 4185 mm
"Structure ", 350 kg, 3595 mm
" Tank ", 70 kg, 4185 mm
" Pump ", 150 kg, 4685 mm
" Water ", 1500 kg, 4185 mm

The result of accumulation is;
Item, front axle, rear axle, gross vehicle mass
Front tare 2655.00kg 0.00kg 2655.00kg
Rear tare 2655.00kg 1045.00kg 3700.00kg
Structure 2704.34kg 1345.66kg 4050.00kg
Tank 2704.34kg 1415.66kg 4120.00kg
Pump 2686.42kg 1583.58kg 4270.00kg with the tank empty.
Water 2686.42kg 3083.58kg 5770.00kg with the tank full.

Notice that the pump adds weight to the rear axle while reducing weight on the front axle.

 

[jack action]

To find the total load on the rear axle $W_{rear}$:

$$W_{rear} = \frac{\sum{L_i W_i}}{L_{wb}} + W_{rear-empty}$$

Where $W_i$ is the weight of the added component $i$ at a distance $L_i$ from the front axle. $L_{wb}$ is the wheelbase and $W_{rear-empty}$ is the rear axle load of the empty truck. The load on the front axle is simply:

$$W_{front} = W_{truck-empty}+\sum{W_i} - W_{rear}$$

Where $W_{truck-empty}$ is total weight of the empty truck and $\sum{W_i}$ is the total weight of the added components.

 

[Baluncore]

Input data.
M kg x mm item
2655, 0, "Tare, front axle. "
1045, 4185, "Tare, rear axle. "
400, 3595, "+ Structure, 300kg + 100kg sheet. "
70, 4185, "+ Empty tank, 70kg. "
150, 4685, "+ Pump. With dry tank, no crew. "
1500, 4185, "+ Water. Full tank, no crew. "
225, -250, "+ 3 crew in front. "
300, 1200, "+ 4 crew in rear. Fully laden. "

Output data.
Front axle Rear axle GVM Item
load kg load kg kg
2655.0 0000.0 2655.0 Tare, front axle.
2655.0 1045.0 3700.0 Tare, rear axle.
2711.4 1388.6 4100.0 + Structure, 300kg + 100kg sheet.
2711.4 1458.6 4170.0 + Empty tank, 70kg.
2693.5 1626.5 4320.0 + Pump. With empty tank, no crew.
2693.5 3126.5 5820.0 + Water. Full tank, no crew.
2931.9 3113.1 6045.0 + 3 crew in front.
3145.9 3199.1 6345.0 + 4 crew in rear. Fully laden.
These are within the manufacturer's maximum axle load specifications.
3600.0 5800.0

 

[MasterG]

Thank you both very much.
I'm going to use the equation that "Jack action" wrote because it is pretty simple and I get it...and these are the results I got earlier when I tried to calculate it myself

for rear and front axle:

http://oi59.tinypic.com/xgmhvs.jpg

Jack action, so considering this results we are good and well within truck official weight limits? official Front and Rear limits are F= 3600kg R=5800kg

 

[jack action]

Jack action, so considering this results we are good and well within truck official weight limits? official Front and Rear limits are F= 3600kg R=5800kg

What can I say? The numbers you calculated are lower than the limits you gave. I don't know if «you» are good (After all, you are the one paid for the job), but this is the theoretical method to find the CG horizontal location.

That being said, some numbers in your last figure are different from the ones you presented:

• 3595 mm vs 3850 mm
• 2655 kg vs 2850 kg
• 2655 + 1045 kg vs 5540 kg
• 300 + 100 kg vs 350 kg

Also, as @Baluncore pointed out, you talk about an empty tank that have a mass of 20 kg and you seem to assume it is 70 kg in your calculations.

 

[MasterG]

yes sorry, I figured it out that I had some different numbers, I'm about to upload the updated version.
The empty tank is around 20kg it is from fiberglass, and it is very light but just to be sure @Baluncore suggested to set it at 70kg, so just to be sure I did input 70kg :)

• 3595 mm vs 3850 mm --> 3850 is the length of the structure, not the distance from front axle which is 3595mm
  
• 2655 kg vs 2850 kg --> 2655kg is the weight of the FRONT axle PRIOR to modifying according to IVECO official documentation sheet, and 2850kg is the actual weighted REAR axle on scale AFTER modifying
  
• 2655 + 1045 kg vs 5540 kg --> 2655kg is the weight of the FRONT axle PRIOR to modifying according to IVECO official documentation sheet, and 1045kg is for the REAR axle PRIOR to modifying according to IVECO official documentation sheet, 5540kg is the actual overall weight of the EMPTY (no crew, no water in tank) truck weighted on scale AFTER modifying it
  
• 300 + 100 kg vs 350 kg --> I forgot about the sheet metal so 300 (structure) + 100 (sheet metal) = 400kg, don't know where I got 350kg though, my mistake

this is why I have problems in the first place :D !
when to use tare, unladen, prior to modifying, kerb, empty truck weight in these formulas ??

 

[MasterG]

Just to be sure about the ACTUAL weights of the truck front and rear axles, we weighted them on scale and the results are:
WITHOUT ANY WATER IN TANK (without crew)
front axle 2690 kg
rear axle 2850 kg
WITH WATER IN TANK (without crew)
front axle 2910 kg
rear axle 4160 kg

these are the results of finished truck
so considering this, why do I even have to calculate if I have the results of the scale?

the overall weight of the truck with full tank of water is 2910+4160=7070kg and the manufacturer states it is an 8000kg vehicle
the weight of the front axle with full tank of water is 2910kg and the manufacturer states that limit of the front axle is 3600kg
the weight of the rear axle with full tank of water is 4160kg and manufacturer states that limit of the rear axle is 5800kg

So there is no mistake that we are within manufacturer limits according to the scale

add the crew of 225kg in first row, and 300 in second row
and we are left with 405kg of equipment like fire hose, helmets and all that (not my problem)

 

[Baluncore]

My calculations show, no water, no crew weights are; front = 2693.5 rear = 1626.5
Your scale weights show; front = 2690.0, rear = 2850.0 ?
Where do the extra rear (2850.0 – 1626.5) = 1223.5 kg come from ?

My calculations show, with water, no crew weights are; front = 2693.5 rear = 3126.5
Your scale weights show; front = 2910.0, rear = 4160.0 ?
Where do the extra rear (4160.0 – 3126.5) = 1033.5 kg come from ?

Your weighed GVM 5540.0 kg compared with my 4320.0 kg.
Where do the extra rear ( 5540.0 – 4320.0) = 1220.0 kg come from.

Did the truck come with a 1200 kg flat tray that you have not included in the calculations ?
You should weigh the truck on the scales before modification.

 

[MasterG]

Yes I understand we had to scale it before, but like I said it is a new job I got, I was just a 3D modeler before so I had no say in scaling and engineering of it.
They showed me the truck and I had to make blueprints, and 3D model out of it.

That is why I have so much trouble now with this calculation :/ basically I'm f****.
And when they went to scale it they put some of the equipment into truck (again, it was before I was on this job) maybe that is from where added weight come from, but I highly doubt it was over 1 ton of weight though :/

and trust me I'm more frustrated then ever because of this static calculation ! I'm trying to figure it out over a week now !
I'm going to try to get more info ASAP and get back to you. It doesn't make sense to me eitherEDIT:
oh, and thank you for trying to help me, seriously, thank you

 

[jack action]

when to use tare, unladen, prior to modifying, kerb, empty truck weight in these formulas ??

When I say «empty truck», I mean the weight of the truck without the tank, the pump, the sheet metal, the structure and - obviously - the water.

so considering this, why do I even have to calculate if I have the results of the scale?

I think that's the question that everybody is asking himself.

 

[MasterG]

like I said, there is no point in my opinion...but they keep pressuring me to make a calculation...so I just MUST do it.
But to be honest, I don't even care much now...I'll just write down the actual weight of the scale and give them that info that is obviously within manufacturer limits.

When I say «empty truck», I mean the weight of the truck without the tank, the pump, the sheet metal, the structure and - obviously - the water

thank you for the explanation, I thought it was just an empty truck (without equipment, crew, water in tank), with all the modification though.