MATHEMATICAL MODELLING

VEHICLE MODELLING

HERE WE WILL BE MAKING MATHEMATICAL MODEL OF THE VEHICLE. IT IS AN ESSENTIAL PART OF DESIGNING BECAUSE IN A MATHEMATICAL MODEL WE CAN CAPTURE THE PHYSICS INTO THE MODEL THAT GIVES A HUGE ADVANTAGE TO THE DESIGNER TO ANALISE THE EFFECT OF VARIOUS PHYSICAL FACTORS INDIVIDUALLY AND TOGETHER. THIS HELPS US TO GIVE STABILITY TO THE VEHICLE EVEN IN WORST SITUATIONS ALSO ONE OF THE BEST FEATURE OF MATHEMATICAL MODELLING IS THAT BY USING IT WE CAN ACTUALLY MAKE THE THING BEHAVE AS WE WANT EVEN THOUGH THE PHYSICAL LAWS MAY TRY TO DO SOMETHING ELSE.

LET US SEE HOW TO MAKE A MATHEMATICAL MODEL WITH A REAL LIFE EXAMPLE OF A BIRD FEEDER. LET THERE BE A RIGHT CYLINDRICAL BIRD FEEDER (WITH 6 FEEDING HOLES 3 HOLES AT THE BOTTOM AND ANOTHER 3 HOLES AT THE MID WAY) AT YOUR GARDEN. YOU WANT TO MAKE SURE THAT THE FEEDER IS ALWAYS FULL OF FOOD FOR THE BIRDS AND YOU DON’T WANT TO FILL IT AFTER SMALL INTERVAL OF TIME EVEN WHEN IT IS NOT EMPTY.

NOW ONE DAY IN MORNING YOU FILL IT FULL AND OBSERVED THAT IT WAS HALF EMPTY WITHIN 30MINS WHEN ALL THE 6 FEEDER HOLES WERE CONTINUOUSLY BEING USED. SO TO MAKE A MATHEMATICAL MODEL WE HAVE ENOUGH DATA AND FROM THAT WE CAN VERY EASILY PREDICT IN HOW MUCH TIME THE FEEDER WILL BE EMPTY IF IT IS BEING USED TO ITS FULL CAPACITY FOR REST OF THE TIME.

½ OF THE FEEDER IS EMPTY IN 30MINS WHEN 6 FEEDER HOLES WERE USED SIMULTANEOUSLY.

NOW AFTER 30MINS THE RATE OF CONSUMPTION WILL CHANGE AND IT WILL REDUCE TO ½ OF THE EARLIER. SO NEXT HALF WILL BE EMPTY AFTER 60MINS IF FOOD IS CONSUMED REGULARLY. SO WE HAVE FOUND THAT IT WILL TAKE A TOTAL OF 30+60=90MINS TO EMPTY THE WHOLE FEEDER.

THAT SHOWS THE IMPORTANCE OF THE MATHEMATICAL MODEL IN OUR EVERYDAY LIFE. SO WHEN WE ARE DEALING WITH AN ENGINEERING DESIGN IT WORKS AS A TOOL FOR THE DESIGNER IN FIXING THE VARIOUS PARAMETERS OF THE DESIGN.

NOW LET US LOOK AT THE MATHEMATICAL MODELLING OF THE VEHICLE.IT IS BASICALLY DONE IN THREE WAYS

1.       FULL VEHICLE MODELLING  

2.       HALF VEHICLE MODELLING

3.       QUARTER VEHICLE MODELLING

IN FULL VEHICLE MODEL THE WHOLE VEHICLE IS CONSIDERED IN 3D SPACE AND THEN MATHEMATICAL MODEL IS DEVELOPED.

IN HALF VEHICLE MODEL WE HAVE THREE HALF VEHICLE MODEL ONE IN THE FRONT VIEW, OTHER ON THE SIDE VIEW AND IN REAR VIEW.

IN QUARTER VEHICLE MODEL INDIVIDUAL WHEEL IS TAKEN AS A SYSTEM AND THEN ITS INDIVIDUAL MODEL IS DEVELOPED.