## 2015/03/01

### Going Direct Drive, take 3 !

In my last post, Going Direct Drive - II, I have shown a few numbers on different scenarios where each scenario represented 4 different designs of the quadrupole motor.
However, I was unclear if each different design of quadrupole motor were powerful enough to move my Toyota Yaris. Now, since I know the available torques with different design, it’s now time to calculate the required toque and power according to the vehicle mass and parameters imposed in the design. From there, it will be easier to design the motor’s minimum specifications.
Also, a lot was to deal with the weight and the mass definitions. Reviewing a few of my notes and searching on the internet for some of my un-answer questions, I finally found does answer about the weight and mass. As an example, when you take the weight on a scale, you are not measuring your weight but your body mass! Weights take into account the gravitational pull and the unit should not be in pound not kilogram.
Because there was a lot of confusing around the mass and the weight, mass is express in kg (lbs) and weight will be express in N or kg/m2 (lbs ft) in this blog.
First, a few data about the car.
 Description Symbol Target / requirements Gross Vehicle Mass (GVM) mv 1 515kg (3 300 lbs) Vehicle rolling resistance (excellent / fair / poor) cr 0.008 / 0.015 / 0.03 Vehicle average acceleration av 1.85 m/s2 (6.069 ft/s2) Vehicle acceleration time ta 15 s Vehicle maximum speed (at 1% grade slop) vv 39 m/s (140 km/h – 87 MPH) Vehicle frontal area Av 1.9 m2 Vehicle drag coefficient cd 0.29 Rolling radius R 0.302 m (P175/65R14 tires) Number of driven wheels nv 2

Three important forces act on the vehicle and are calculated according to these formulas.
The natural force or the actual weight in N
(1)   Fn = m g sin (ϴ)
The rolling resistance force of the tires:
(2)   Fr = Fn Cr cos (ϴ)
The aerodynamic drag force:
(3)   Fd = ½ ρ cd A v2
And the slope:
(4)   F = Fn + Fr + Fd
Power requirement on a 1% slopped road and 100km/h (acceleration is null):
First, let’s start by calculating the power requirement. The equation is below:
(5)   P = F v
P is the mechanical power in watt (W) and v is the speed in m/s. The total force (whitout acceleration) while be 854.7 N. So the power requirement for a speed of 100km/h (27.8 m/s) will yield at 23 760W.
For a 2 wheeler, each will have to power half of the total force which is 11 880 W. This is nominal or minimum power to move my Toyota Yaris.
To covert speed (linear velocity) to rev/s (rotational velocity), we simply use equation 5 below:
(6)   ωw = v / rw
Where v is the linear velocity of the car in m/s and rw is the radius of the wheel in m.
In a worksheet like excel, I’ve put in does numbers and plotted the trend that is shown here.

For a speed of 100 km/h, the power requirement is 23 740 W. For each wheel, it will yield to half the power; 11 870 W.
Below, the force required per wheel is plotted below. At 100km/h, the force yields to 427N.

Below is the torque per wheel trend.

Let’s compare this to the 4 scenarios of my last post.
First, the power capability of the quadrupole is calculate from this equation 76.
(7)  Pe = Te Gr v/rwheel
Where Pe is the power from the electric motor, Te is the torque capability of the motor in Nm, Gr is the gear ratio between the wheel and the motor, v is the vehicle velocity in m/s and rw is the radius of the car wheels traction in m. The gear ratio is 1:1 (1) since there is no gear reduction between the motor and the wheels.
 Electronic speed RPM rad/s Te Gr rw v Pe = Te Gr V/rw Scenario 1 1st  e-speed 3327 348,4 39,3 1 0,305 16,9 13 691 2nd e-speed 5742 601,3 22,8 1 0,305 29,2 13 709 3rd  e-speed 7676 803,8 17 1 0,305 39,0 13 664 RPM rad/s Te Gr rw v Pe = Te Gr V/rw Scenario 2 1st  e-speed 1746 182,8 37,4 1 0,305 8,9 6 838 2nd e-speed 3058 320,2 31,4 1 0,305 15,5 10 055 3rd  e-speed 3698 387,2 17,7 1 0,305 18,8 6 854 RPM rad/s Te Gr rw v Pe = Te Gr V/rw Scenario 3 1st  e-speed 950 99,5 34,4 1 0,305 4,8 3 422 2nd e-speed 1679 175,8 19,5 1 0,305 8,5 3 428 3rd  e-speed 2076 217,4 15,7 1 0,305 10,6 3 413 RPM rad/s Te Gr rw v Pe = Te Gr V/rw Scenario 4 1st  e-speed 921 96,4 70,9 1 0,305 4,7 6838 2nd e-speed 1614 169,0 40,5 1 0,305 8,2 6845 3rd  e-speed 1952 204,4 33,5 1 0,305 9,9 6847

So, all current designs do not meet the requirements excepted for Scenario 4 at first speed but I will never be able to reach top speed of 140 km/h because the load per wheel needs to triple. In scenario 4, the current is set at 50A load. I will need at least 222Nm of torque to reach the top speed of 105 km/h. The currents designs cannot handle that much current. So, one easy thing to do is to triple the depth of the motor; passing from 76mm to 228mm, almost 9 inch long.
But, the quadrupole was first design to handle speeds up to 6000RPM and to be connected to a reducing gear like a car transmission and differential.  Also, I have another project; I intend to build an XR3 3 wheeler vehicle from Robert Q. Riley Enterprises. According to their specifications, the Scenario 4 will do the job because I need 13 kW to reach 140 km/h. So with minor modifications such as adding winding to the outer stator will enhance the MMF.