If you’re a car enthusiast who loves shifting gears in a manual transmission then this article is for you. We enjoy the mechanical process of selecting just the right gear for the most power and thrill of being in control. The art of double clutching is still used today by first class racing drivers. Here’s why: The driver does not want to upset the balance of the car when downshifting prior to the upcoming turn. He or she sees the turn coming up and knows that second gear will be needed to accelerate at the turns exit. So, while braking, the driver decides to downshift to “prepare” for the turn. Full brake efficiency is needed to slow the car down and the driver cannot afford to lock the drive wheels due to a poor shift. What does he or she do? A double clutch. Good on ya! Here’s why it works.
Conservation of momentum
As mentioned above the driver cannot tolerate a shock to the drive wheels due to the downshift. Lets consider the momentum of the car during the downshift and the time it takes to shift, maybe 1-2 seconds max. Our driver, Ralph, wants to learn how to learn how to downshift more efficiently so he is practicing a downshift from third to second. The car is travelling in third gear at 60 mph at 3800 RPM shifts to second gear. (5000 RPM). To keep the math simple Ralph is not applying brakes because he’s practicing just the shift. Lets assume the time it takes to shift from third to second is 1.5 seconds and the speed of the car remains at 60 mph. Or so he hopes. Ralph knows that he doesn’t want to add any braking torque to the driven wheels because that will upset the cars balance. Question: What happens when Ralph does a conventional downshift versus a double clutch downshift?
The car has both kinetic energy (1/2mV2 ) and rotational energy in the drivetrain (1/2Iw2 )
Let’s break up the drivetrain into three major components:
- Mass A Driven wheels and everything physically connected to them. Tires, wheels, brake rotors, axles, differential, and output shaft inside the transmission are all spinning together. Brake calipers don’t spin for example, but they are accounted for in the car’s kinetic energy.
- Mass B Transmission Input shaft and gears connected to it. This is mostly mass inside the transmission. Let’s assume 16lbs of weight that needs to rotate.
- Mass C Engine Parts. This included the pressure plate, flywheel, crankshaft, rods, cams, etc.
First the conventional shift: Ralph presses the clutch and takes the car out of third and is on his way to second gear. The car is momentarily in neutral: Let’s pause here for a minute before Ralph selects second gear.
What happens to the momentum of Mass A, B, and C (conventional shift)?
Mass C slows down because Ralph is not on the gas and the engine is disconnected from the wheels (engine goes down to 1000 RPM when clutch is depressed)
Mass B rotational speed decreased because Ralph is in neutral temporarily. Let’s assume it drops to 1000 RPM as it is just coasting in a splash zone of oil.
Mass A rotational speed remains the same as does the cars speed (60 mph). (let’s forget about rolling friction and wind drag for the short time it takes to shift gears)
Second gear is selected (conventional shift)
Mass C engine speed is unchanged.
Mass B rotational speed of the input shaft goes up because the synchros speed up the input shaft as required to get into second gear. The speed of the input shaft went from 1000 RPM to now 5000 RPM. (2nd Gear at 60 MPH)
Mass A rotational speed of the car’s wheels goes down because the energy had to come from somewhere to speed up mass B.
When Ralph changes from third gear to second gear the energy redistributes between the masses A,B, & C.
En=1/2mV602 + 1/2Iwn2 +1/2IAwA2
E2 = 1/2mV2 + 1/2IBw22 + 1/2IAwA2
E2=En + Ef
Ideally energy would be conserved when downshifting from 3rd to 2nd, however the synchros work by friction to soften the collision between 3rd and 2nd gears. This takes energy and creates heat too. Note: Ef is assumed to be 50% of the energy needed to accelerate the input shaft Mass B from 1000-5000 RPM.
If you’re still hanging with me, you’ll remember that the goal during downshifting was not to shock the wheels and loose momentum during the shift. Using the equations above, I can solve for the new velocity after the shift.
Here are the numbers I used, IB = .005 kg-m2 (3″ diameter by 8″ steel cylinder to approximate the trans input shaft and attached gears.
The new speed of the car is 59.9 MPH and the Ralph hasn’t even let the clutch out in second gear. (We lost 0.1MPH from 60 MPH)
The amount of torque required to accelerate mass B from 1000 RPM to 5000 RPM is calculated from Newton’s Second Law
T=dL/dt which says the external torque is proportional to the rate of change of momentum
For small periods of time we can approximate this as T=I(w3-w2)/(t3-t2)
t3-t2 should really be the time it takes to go from neutral to second gear. So I used .75 seconds here. The other .75 seconds was used to go from third to neutral. In a normal shift there wouldn’t be a pause in neutral, but bare with me.
This requires an average torque of 2.1 ft-lbs to bring mass B up to speed applied over 0.75 seconds.
Likely this torque spikes up at the very beginning and shocks the rear wheels with a torque multiplied by the gear ratios. The drive ratio in second gear is 6 to 1. Ralph experiences 18 ft-lbs of torque applied at the driven wheels by selecting second gear alone.
As soon as Ralph lets the clutch out, some of the cars remaining energy must speed up Mass C (the engine to 5000RPM)
The equivalent rotational inertia of a small sports car engine is around 0.3 kg-m2
E2o = 1/2mV2 + 1/2IBw22 + 1/2IAwA2 +1/2ICwC2
Solving for the new cars velocity in 2nd gear after the clutch is let out (E2o) is: 56.2 MPH
As stated earlier this is an undesirable result causing additional braking to the driven wheels that can upset the car’s balance or weight transfer. The car lost 3.7 MPH just by letting the clutch out and revving the engine with the wheels. That’s a lot deceleration in only 0.75 seconds and will likely cause a spin if already on the brakes!
Now let’s look at what Ralph could do by introducing the double clutch technique:
Ralph has another form of energy at his disposal. We didn’t talk about chemical energy, but lets not forget about the gas in the tank and Ralph’s gas pedal. Bingo! Rather than loose energy to the synchros and the driven wheels, Ralph can add energy as needed with the gas pedal!
The right time to add energy is right before second gear is engaged, Ralph blips the throttle while the car is in neutral.
Now instead of relying on the driven wheels to speed up the Mass B, Ralph lets the clutch out while still in neutral. This takes energy from the engine Mass C and speeds up the input shaft Mass B.
Then when Ralph selects 2nd gear no energy is lost!
When Ralph lets the clutch out in second gear the engine is still spinning due to the throttle blip so no energy is needed to speed up the engine either.
The result if done perfectly is a car that continues along at 60MPH despite a gear change.
Now of course, the car will begin to decelerate in second gear because there are pumping forces, and frictional forces that the engine exerts to the driven wheels. As Ralph goes down in gears the ratios get higher so these frictional and pumping forces will slow the car down at a faster rate.