Physics Behind Motion

 For understanding, let’s assume

• Vehicle is on flat ground; No Gradient.

Remember First Law of Motion? - Newton's Law of Inertia

• An object will continue to be in the state it is in (be it at Rest or in Motion) untill acted upon by an External force.

So, in case of vehicles, to break the state of Rest, we need some force, called "Tractive force: Ftractive"

• How Much?
• Ftractive > Static Rolling Resistance (Frr_static)
• Frr_static = mtotal * g * µrr_static
• mtotal: Vehical Mass/Total Mass Required to be put into motion
• µrr_static: Coeff. of Rolling Resistance (Static)

Source of force?

• Prime Mover

                Engine

                Electric Motor (E-Machine)

Why do we need Gearing?

• Prime Mover Needs force or speed Multipliers

                  Depending upon vehicle's state

                         Break Rest/Overcome an Obstacle -> Force

                         Speed -> When Vehicle is in motion

• Gears do Exactly that 

As discussed above:- Ftractive> Frr_static

• To move vehicle from Rest
• But, to break 'Rest', we need Ftractive= Frr_static
• Where does the additional force go?

                   It will accelerate the vehicle by:-
                           a = (Ftractive - Frr) / (mass * γ) ; Ftractive - Frr = Fnet

                            γ -> Equivalent mass factor

Basically, we are accelerating mass along with overcoming the rotational Inertia
 γ = 1 + (Inertia_of_wheels / (m * rdyn²)) + ((Internal_Inertia * (Gear_Ratio_total)²) * η) / (m * rdyn²))

       m: Total Mass (Kg); η: Driveline Efficiency; rdyn: Tire Dynamic Rolling Radius(m)

So, does that mean once the static Inertia is Broken, the vehicle will keep on accelerating?

• NO

Once vehicle is in motion, 2 forces act on the Vehicle

• Rolling Resistance (Natural Break)
• Aerodynamic Drag
• These are the forces that stop the vehicle when we lift the foot off the Acceleration Pedal
• Vehicle stops Accelerating when below forces balance:-
   Ftraction_dynamic = Frr_dynamic+ Fdrag
• First law keeps the vehicle moving @ constant speed.

While driving your Car, you might have noticed, on flat road you can break vehicle's static Inertia even in 2ndGear (or sometimes in 3rd gear depending upon the conditions), and can upshift from 2nd to 4th but not on a gradient (or hills), because of additional mass component acting.

Hence, the selection of subsequent gears matter.

• Engines are designed to work @ Rated Power
• Engine Torque @ Rated Power = Peak Torque - "Back-up Torque"

Mental Visualization:- If your car moving at Engine Rated speed hits a bump/obstacle, It’s speed slows down, looking at the engine torque curve, you'll see that basically Engine trades off speed for torque to overcome the obstacle.

If vehicle overcomes the obstacle, using the Back-up Torque available:

• "Great!!" -> It accelerates again
• Otherwise -> "Engine stalls!"

What you are actually doing while down-shifting

• Basically, depending upon the Gear Ratio, You are tuning (Bumping-up) Engine RPM to use Engine Torque upstream of Maximum Torque Engine RPM.

Note: The torque at the Wheels is dictated by the Traction Limit.  F_tractive_max = m * g * µ_peak; If the Engine produces more Torque than the Traction Limit, the wheels will just slip - a kind of acting as a fuse preventing the driveline from overloading. 

Designing Gear Ratios

For smooth shifting, the vehicle speed between the 2 subsequent gears should overlap by 10% to 20% (depending upon the vehicles you are dealing with i.e. Tractors or Cars; Cars have generally higher Overlap, can go ~30%).

          Why?

• If you look at the sample saw Tooth Curve (along with the Engine Curve), the vehicle is in the right operating zone when the Engine RPMs are above Peak Torque RPM.
• Now, when you start the vehicle in 1st Gear, you accelerate the vehicle (post static Inertia Break) from Idle, to Peak Torque RPM & beyond.
• Somewhere around Rated Power RPM or Maximum, the driver generally upshifts.
• As you'll upshift, depending upon the Total Gear Ratio of the next gear, the Engine RPM will Drop (immediate post upshift)

For smooth operation the Engine RPM after this drop "should" still be > Engine Peak Torque RPM

• Why?

                Because, the engine will be operating in it's stable zone -> smooth vehicle operation!

                In case of obstacle, Engine will have Back-up Torque.

What if the speed fall below Max. Engine Torque speed, during upshift?

• Vehicle is in motion
• Engine will Not be in it's stable zone (Post upshift) (See the sharp decline of the Engine Torque curve on the left side of the Max. Engine Torque)

If Ftraction_dynamic > Frr_dynamic+ Fdrag

• Vehicle will remain in motion but you may feel lag (you might have experienced it while driving car, if you have ever tried aggressive upshift, like 2nd Gear to 5thGear).
• If Ftraction_dynamic< Frr_dynamic + Fdrag
• Engine stalls

You can very well imagine, why you can sometime successfully upshift from 2nd to 5th gear (your car) on flat road, but not on a gradient.