What is the procedure for the calculation of the diameter of the drive shaft of a BAJA buggy?

Yes, there is a procedure in our design book.

If you are going to build a BAJA buggy you have to go reverse that is by applying Market availability of drive shaft. Whatever you calculate is impractical or not available in the market. So the best procedure is to do a market study and then decide. Do reverse engineering. The overall calculation is based on torque and speed. Always remember your theoretical knowledge is important but not always useful for practical purposes.

What are the powertrain calculations for the E-Baja competition?

It is similar to m-BAJA powertrain calculation.

First of all, you should find drag forces on the vehicle then find out the torque on wheels, after that decide your reduction on the basis of your motor output torque. Its depend on you that which type of transmission system you choose (auto or manual). Then find your acceleration, top speed and gradeability of vehicle.

For the basics take help from fundamental of vehicle dynamics by Thomas d. Gillespie and for coefficients and constants take help from google search engine.

How to Calculate forces coming on Knuckle

Steering knuckle is the most stress sustaining and critical component of All Terrain Vehicle (ATV). Steering knuckle is the pivot point of the steering and suspension system, which allows the front wheels to turn and also allow the movement of suspension arms motion. The light weight and high strength component is always in demanding for racecar application.
Lightweight and optimized design of steering knuckle is proposed to use for a BAJA SAE INDIA off road racecar. Due to the failure in knuckle in terrain vehicle after some instances, it has to be modified for better performance. The 3D CAD model created by using CATIA V5 and static as well as model analysis carried out in ANSYS 12 to understand its behavior under operating conditions. All test for frame was carried out on aluminum alloys 6061-T6 & for spindle EN8. The paper discusses the FE analysis of existing and modified Steering Knuckle.

Calculation of Load:

Axial Loads
The two major loads acting on the knuckle are Tensile and
Compressive loads. The stresses due to these loads can be
determined using the following formulas
Tensile Load (Pt) = Tensile Stress X Area
Compressive Load (Pc) = Compressive Stress X Area
Inertia Load
This load is due to the inertia of the moving parts. To calculate
the inertia force, first two harmonies are taken into
consideration. It is given by,


All-Terrain Vehicle (ATV) – NVH (Noise Vibration & Handling) Control

Good NVH is becoming must feature in recent commercial vehicles. One of the major discomforts caused to driver by Engine vibration during idling. The power train is suspended on the vehicle frame on several flexible mounts, whose purpose is to isolate the vibration between engine and frame. Total 6 different modes of Engine like roll, yaw, pitch and Vertical, lateral and longitudinal need to isolate. Engine mount stiffness and position is critical and need to have methodology to verify in early stage of designing [1].

In this paper, the stiffness and modulus of elasticity value of engine rubber mount is calculated experimentally by carrying out compressive test on UTM. Later, the critical frequency is found by carrying modal analysis on this engine mount through ANSYS. Also by doing calculation, the position of driver’s seat is found ensuring the minimum NVH condition.

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In this paper, Transfer Path Analysis (TPA) method has been used to reduce the vibration at the seat of an All

Terrain Vehicle (ATV). The vibration source considered is the engine. Modifications are made on an existing Baja roll cage and comparisons are made to the existing design to arrive at the optimized design.FE model of the roll cage is analyzed and experimental validation is done.Modifications in the Transfer Path change the vibration pattern at the receiver. The modifications include addition of new roll cage members and use of different cross sectional beams for the engine mount. These changes result in reduced transmission of vibration from the engine to the roll cage. The analysis has been done in three different RPM ranges of the engine in order to ensure that a particular modification gives good performance over the entire operating range of the engine.

White Paper – Download

Nowadays, in automotive industry the vehicle design cycle is mainly ruled by the highly competitive nature of the market and the ever increasing customer demands and expectations. This challenges automotive manufacturers to achieve higher-quality products in ever shorter time frames, while at the same time, reduce the design costs. This can only be achieved when the design cycle takes place largely on the basis of virtual modeling and simulation such that the traditional test phase, which relies on expensive and time-consuming physical prototypes, can be drastically shortened. As a result, nowadays, each stage of the design cycle is supported by CAE (Computer Aided Engineering) methodologies which allow to predict various functional performance attributes, such as NVH (Noise, Vibration & Harshness), crashworthiness, etc. Moreover, researchers have developed many techniques to speed up the calculations, enabling efficient modification approaches and optimizations. This paper focuses on the vehicle interior NVH performance. For a vehicle body Finite Element (FE) model, a reduced formulation has been achieved by using the WBS (Wave-Based Substructuring) technique. More specifically, a modification approach has been applied that is based on the generation of bead patterns on a subcomponent that has been identified as critical for the NVH behavior. By combining the reduced structural model with an efficient ATV (Acoustical Transfer Vector) approach to predict the interior acoustics performance, one can efficiently evaluate the effect of structural modifications on the interior NVH levels, such that the global NVH behavior can be optimized. The main innovation introduced in this paper comprises the optimization of vehicle vibro-acoustics by making use of a structural optimization software in combination with an acoustic target function. Two different methodologies have been worked out, based on two strategies for bead pattern optimization. Finally, the optimized component has been evaluated in terms of radiated Sound Pressure Level (SPL) and manufacturability.

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Fundamentals of Brake Calculation

Brake Calculations

There are many books on brake systems but if you need to find a formula for something in particular, you never can. This page pulls them together with just a little explanation. They should work for any two axle vehicle but it’s YOUR RESPONSIBILITY to verify them. Use them at your risk…..




Static Axle Load Distribution

Note: this changes with the loading of the vehicle so laden and unladen figures are often different.

Relative Centre of Gravity Height

Dynamic Axle Loads (Two Axle Vehicles Only)

The changes in axle loads during braking bears no relationship to which axles are braked. They only depend on the static laden conditions and the deceleration.

Note: The front axle load cannot be greater than the total vehicle mass. The rear axle load is the difference between the vehicle mass and the front axle load and cannot be negative. It can lift off the ground though. (Motorcyclists beware)!


Braking Force

The total braking force required can simply be calculated using Newton’s Second Law.

Wheel Lock

The braking force can only be generated if the wheel does not lock because the friction of a sliding wheel is much lower than a rotating one. The maximum braking force possible on any particular axle before wheel lock is given by:


Brake Torque

Having decided which wheels will need braking to generate sufficient braking force the torque requirements of each wheel need to be determined. For some legislation the distribution between front and rear brakes is laid down. This may be achieved by varying the brake size or more likely using a valve to reduce the actuation pressure.



Disc Effective Radius

The effective radius (torque radius) of a brake disc is the centre of the brake pads by area.
For dry discs it is assumed to be:


For full circle brakes it is:

Note: the difference is because full circle brakes contact on the full face but caliper pads are not usually a quadrant but have square sides (Given the variability of friction the difference is not important in practice).


Clamp Load

The clamping load is assumed to act on all friction surfaces equally. For dry disc brakes it doesn’t matter whether the brake is of the sliding type or opposed piston. Newton’s Third Law state every force has an equal and opposite reaction and a reaction force from a sliding caliper is the same as an opposed piston one.


Brake Factor

Ball ramp brakes have a self servoing effect rather like a drum brake. The brake factor multiplies the output torque.


Brake Sensitivity

High factor brakes become very sensitive to manufacturing tolerances and lining friction variations. A measure of sensitivity is the amount the brake factor varies for a change in lining friction. It can be calculated:



System Pressure

Pressure is a function of the required clamp load and the piston area. Remember on an opposed piston disc brake it’s only the area on one side of the disc.

Servo Booster

Servo characteristics are defined graphically. The output will have at least two slopes but will also have a dead band at the bottom.

Pedal Force

The pedal ratio is calculated to the centre of the foot pad. The pedal return springs may make a significant contribution to the overall pedal force. Especially at full travel.


The deceleration used in calculations is a steady state one called MFDD (mean fully developed deceleration). It assumes the vehicle is either braking or not. In practice it takes a time for the system pressure to rise and the friction to build up. This is not the driver reaction time but the system reaction time. Where a calculation requires a stopping distance or an average stop deceleration then this delay must be taken into account. For calculations a linear build up over 0.6 second is used ie 0.3 second delay.

For testing the following graph show the requirements for 71/320/EEC and ECE R13.


Stop Energy

The energy dissipated in a stop is the sum of energy from three sources, kinetic, rotational and potential.

Kinetic Energy

Assuming the stop is from the test speed down to zero then the kinetic energy is given by:-

Rotational Energy

The rotational energy is the energy needed to slow rotating parts. It varies for different vehicles and which gear is selected however taking 3% of the kinetic energy is a reasonable assumption.

Potential Energy

The potential energy is the energy gained or lost by stopping on a hill.

Braking Power

Only when the brake is applied (but rotating) is energy being dissipated in the brake system. Some of the stop energy is dissipated in the tyre as wheel slip. Managing the ideal wheel slip is the ultimate goal of ABS development but here assume 8%. The energy to each brake depend on the number of brakes and the proportion of braking on each axle.

In order to calculate the power we need to know the brake on time:

The power is then given by:

This is the average power, the peak power at the onset of braking is double this.

Dry Disc Temperature Rise

These calculation are based on that given in the following reference:

Brake Design and Safety 2nd edition by Ruldolf Limpert

Single Stop Temperature Rise

In order to approximate the temperature rise of the disc an assumption as to where the energy is going has to be made. Initially most of the heating takes place in the disc, however this can then be rapidly cooled by surrounding components and the air stream. The calculation assumes 80% goes to the disc.

Heat flux into one side of the disc:

Single stop temperature rise is:

Fade Stop Temperature Rise

The temperature rise after repeated stopping can also be approximated, although so many variables exist it is suggested this is only used for basic optimisation work.

After a number of stops:


Axle Loads

When parking on an incline the lower axle has a higher load than it does on the level.

The rear axle load is the difference between the vehicle mass and the front axle load.

Traction Force

If the braked wheel is very light on an incline then it is possible the tyre will slip before the brake. Hill hold is usually required with the vehicle facing both up and down the hill. The traction force required to park the vehicle is:

Where only one of the two axles is braked the limiting slope is:


Cable losses are not inconsiderable and vary depending on the number and angle of bends. A typical cable supplier uses the following calculation to calculate cable efficiency:


Brake Fluid Volume Requirements

When an hydraulic brake is applied fluid is required to move through the pipes. If the fluid source is a master cylinder it has a finite capacity. The following components need fluid:-

Foundation Brake Requirements

Brake fluid is required to take up running clearance.

It is also needed to compensate for lack of stiffness of the brake housing. For a disc brake the following approximation can be used:

Pads Compressibility

Pad compressibility varies between hot and cold conditions. Worst case figures are 2% cold and 5% hot at a pressure of 16MPa. The fluid required is given by:

Rubber Hose Expansion

The rubber hose expansion coefficient is usually taken as

Steel Pipe Expansion

Pipe expansion is very small and unlikely to be of interest however it should be noted that it is proportional to the cube of the diameter, so using bigger pipe than necessary on a system with a fixed fluid volume will cause longer travel for two reasons, the stiffness of the pipe and more importantly the additional fluid compression losses.

Master Cylinders Losses

Fluid losses in master cylinders increase with bore size and pressure. A reasonable assumption can be found by using the following:

Fluid Compression

Fluid compression varies with temperature and the type of fluid used.

The fluid needed to take account of compression is calculated:

It is usual to allow about 3% for trapped air in the circuits that can’t be removed by bleeding. This air is squashed totally flat during braking.


When testing Brakes on a dynamometer it is important to calculate the inertia requirements.
Many brakes do not run at the same speed as the wheels so it is important to understand how the brake will be mounted on the rig.
Ignoring the inertia of the wheels the required dynamometer inertia is given by



Gear Reduction Selection

Power Requirements against:


Fr: Wheel Resistance

FL : Air resistance

Fs: Gradient resistance

Fa: Acceleration resistance


Wheel Resistance= Rolling resistance + Slip Resistance + Road Resistance

Tr: Brake Torque


Assumption taken


Unmade road coefficient of friction fr= .16

mass of vehicle being=Mf




Fr=fr*Mf*g*Cosαst     where αst=30˚


Fr=0.16*200*9.81*Cos 30



Total Load R=113kg(driver)+200kg (vehicle)



Static Resistance=µR




Wheel Radius r=221.875mm

= .221m

Air Resistance



Ρ=Air Density

Cw=Drag Coefficient




FL =0.5*1.99*0.0315*(16.66)2




Gradient Resistance:

Fst=Mf*g *Sinαst


Putting the corresponding value



Acceleration resistance:





Power Required: Ftotal*v/(Nrpm*η)