# US 11,906,396 B1 · System and method of using a mobile device as an aerodynamic testing system and power meter

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- Number: US 11,906,396 B1
- Document ID: US11906396B1
- Status: Granted
- Kind: B1
- Application number: 16/999,903
- Filed: 2020-08-21
- Granted: 2024-02-20
- Earliest claimed: 2019-08-22
- Applicants: William Blake Laing, III
- Inventors: William Blake Laing, III
- Web page: https://patentgrep.com/patent/US11906396B1

## CPC

- G01M 9/06: Measuring arrangements specially adapted for aerodynamic testing
- G01M 9/08: Aerodynamic models
- G01M 17/007: Wheeled or endless-tracked vehicles (G01M17/08 takes precedence)
- G07C 5/008: {communicating information to a remotely located station (transmission systems for measured values G08C)}
- G07C 5/0816: {Indicating performance data, e.g. occurrence of a malfunction}
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G07C: TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE

## Abstract

Methods of determining resistive coefficients of a vehicle include using a force-based analysis method and a work-energy analysis method. The methods include receiving an input on a mobile device to initiate a test protocol along a path. The mobile device records a set of measurements for determining a drag area coefficient and a coefficient of rolling resistance for the vehicle using the force-based or work-energy analysis method. For the force-based analysis method, a direct measurement of proper acceleration of the vehicle is measured from an accelerometer on the mobile device. For the work-energy analysis method, a normal force on the vehicle is determined from a direct measurement of proper acceleration from an accelerometer on the mobile device. The mobile device determines the drag area coefficient and the coefficient of rolling resistance based on the set of measurements using the force-based or work-energy analysis method.

## Claims

### Claim 1

A method of determining resistive coefficients of a vehicle using a force-based analysis method, the method comprising:
receiving, via a mobile application executing on a mobile device mounted to a vehicle, an input to initiate a test protocol along a path;
recording, by the mobile application, a set of measurements for determining a drag area coefficient and a coefficient of rolling resistance for the vehicle using the force-based analysis method, wherein the set of measurements includes a direct measurement of proper acceleration of the vehicle from an accelerometer on the mobile device; and
determining, by the mobile application, the drag area coefficient and the coefficient of rolling resistance based on the set of measurements using the force-based analysis method.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
obtaining, by the mobile application, a local air density and wind speed from a remote weather database; and
determining an air speed based on the wind speed and a ground speed.

### Claim 3 (depends on 2)

The method of claim 2, wherein the ground speed is measured from a speed sensor mounted to the vehicle and in communication with the mobile device.

### Claim 4 (depends on 2)

The method of claim 2, wherein the ground speed is determined based on a plurality of time-stamped location measurements from a global positioning system (GPS) sensor on the mobile device.

### Claim 5 (depends on 1)

The method of claim 1, wherein the test protocol is a coast-down test protocol, and wherein the set of measurements is obtained using only sensors present on the mobile device.

### Claim 6 (depends on 1)

The method of claim 1, wherein the set of measurements further include a power of propulsion of the vehicle measured from a power sensor on the vehicle and in communication with the mobile device.

### Claim 7 (depends on 1)

The method of claim 1, wherein the set of measurements is recorded on a periodic basis, the method further comprising:
calculating, by the mobile application, for each of the set of measurements recorded, an (x, y) value pair based on the corresponding set of measurements to produce a plurality of (x, y) value pairs;
determining, by the mobile application, a line fit for the plurality of (x, y) value pairs; and
determining, by the mobile application, a slope and y-intercept of the line fit, wherein the coefficient of rolling resistance is the y-intercept of the line fit and the drag area coefficient is determined based on the slope.

### Claim 8 (depends on 7)

The method of claim 7, wherein each of the plurality of (x, y) value pairs is calculated by:
y
=
(
p
propel
v
g
+
ma
0
·
||
-
I
R
2
⁢
a
||
)
ma
0
,
⊥
⁢
and
⁢
⁢
x
=
v
air
2
/
a
0
,
⊥
,
where Ppropel is a power of propulsion of the vehicle, νg is a ground speed, m is a mass of the vehicle, a0, ∥ is a component of the proper acceleration in a direction parallel to a surface upon which the vehicle travels, a0, ⊥ is a component of the proper acceleration in a direction perpendicular to the surface upon which the vehicle travels, a∥ is acceleration in a direction of motion, I is a net moment of inertia of tires on the vehicle, R is an average radius of the tires on the vehicle, and νair is an air speed relative to the vehicle.

### Claim 9 (depends on 7)

The method of claim 7, wherein the line fit is determined by one of the group of statistical analysis methods consisting of: linear regression, multilinear regression, multivariable regression, Bayesian inference, digital filtering, and Kalman filtering.

### Claim 10 (depends on 1)

The method of claim 1, wherein the force-based analysis method comprises:
1
2
⁢
ρ
⁢
C
⁢
d
⁢
A
⁢
v
2
+
C
r
⁢
r
⁢
m
⁢
a
0
,
⊥
=
F
resist
=
P
propel
v
a
+
ma
0
,
||
-
1
R
2
⁢
a
||
,
where ρ is air density, CdA is the drag area coefficient, Crr is the coefficient of rolling resistance, m is a mass of the vehicle, νair is an air speed relative to the vehicle, a0, ⊥ is a component of the proper acceleration in a direction perpendicular to a surface upon which the vehicle travels, Fresist is a net resistive force, Ppropel is a power of propulsion of the vehicle, νg is a ground speed of the vehicle, in is a mass of the vehicle, a0, ∥ is a component of the proper acceleration in a direction parallel to the surface upon which the vehicle travels, a∥ is an acceleration in a direction of motion, I is a net moment of inertia of tires on the vehicle, and R is an average radius of the tires on the vehicle.

### Claim 11 (depends on 1)

The method of claim 1, further comprising:
calculating, by the mobile application, a power of propulsion of the vehicle using the drag area coefficient and the coefficient of rolling resistance; and
displaying, by the mobile application, the power of propulsion on a user interface of the mobile device.

### Claim 12

A method of determining resistive coefficients of a vehicle using a work-energy analysis method, the method comprising:
receiving, via a mobile application executing on a mobile device mounted to a vehicle, an input to initiate a test protocol along a path;
recording, by the mobile application, a set of measurements for determining a drag area coefficient and a coefficient of rolling resistance for the vehicle using the work-energy analysis method, wherein a power of propulsion of the vehicle is measured from a power sensor on the vehicle and in communication with the mobile device and
determining, by the mobile application, the drag area coefficient and the coefficient of rolling resistance based on the set of measurements using the work-energy analysis method.

### Claim 13 (depends on 12)

The method of claim 12, wherein a normal force on the vehicle is determined from a direct measurement of proper acceleration from an accelerometer on the mobile device.

### Claim 14 (depends on 12)

The method of claim 12, wherein the set of measurements includes a ground speed, an air speed, and an elevation of the vehicle.

### Claim 15 (depends on 14)

The method of claim 14, further comprising:
obtaining, by the mobile application, the local air density and wind velocity from a remote weather database; and
determining the air speed based on the wind velocity and the ground speed.

### Claim 16 (depends on 14)

The method of claim 14, wherein the ground speed is measured from a speed sensor mounted to the vehicle and in communication with the mobile device.

### Claim 17 (depends on 14)

The method of claim 14, wherein the ground speed is determined based on a plurality of time-stamped location measurements from a global positioning system (GPS) sensor on the mobile device.

### Claim 18 (depends on 12)

The method of claim 12, wherein the set of measurements is recorded on a periodic basis, the method further comprising:
calculating, by the mobile application, for each of the set of measurements recorded, an (x, y) value pair based on the corresponding set of measurements to produce a plurality of (x, y) value pairs;
determining, by the mobile application, a line fit for the plurality of (x, y) value pairs; and
determining, by the mobile application, a slope and y-intercept of the line fit, wherein the coefficient of rolling resistance is the y-intercept of the line fit and the drag area coefficient is determined based on the slope.

### Claim 19 (depends on 18)

The method of claim 18, wherein each of the plurality of (x, y) value pairs is calculated by:
y
=
(
W
pedaling
-
1
2
⁢
(
m
+
I
R
2
)
⁢
(
v
f
2
-
v
i
2
)
-
mg
⁢
(
h
f
-
h
i
)
-
W
other
)
/
(
mI
t
)
⁢
and
⁢
x
=
I
a
I
t
,
where Ia=∫νair2ν dt=∫νair2ds,It=∫ a0, ⊥ν dt=∫ a0, ⊥ ds, and Wpedaling=∫Ppropeldt, where Ppropel is the power of propulsion of the vehicle, νair is an air speed, a0, ⊥ is a component of proper acceleration in a direction perpendicular to the surface upon which the vehicle travels, ν is a speed of the vehicle along the ground, νi is a ground speed upon initiation of a test protocol segment, νƒ is a ground speed upon conclusion of the test protocol segment, in is a mass of the vehicle, hi is the height upon initiation of the test protocol segment, hƒ is the height upon conclusion of the test protocol segment, I is a net moment of inertia of tires on the vehicle, R is an average radius of the tires on the vehicle, g is acceleration of gravity, and Wother is work done by other dissipative forces on the vehicle.

### Claim 20 (depends on 12)

The method of claim 12, wherein the work-energy analysis method comprises:
1
2
⁢
ρ
⁢
CdAI
a
+
Crr
⁢
mI
t
+
W
other
=
W
pedaling
-
1
2
⁢
(
m
+
I
/
R
2
)
⁢
(
v
f
2
-
v
i
2
)
-
mg
(
h
f
-
h
i
)
,
where
Ia=∫νair2ν dt=∫νair2ds,It=∫ a0, ⊥ν dt=∫ a0, ⊥ ds, and Wpedaling=∫Ppropeldt, where ρ is air density, CdA is a drag area coefficient, Crr is a coefficient of rolling resistance, where Ppropel is the power of propulsion of the vehicle, νair is an air speed, a0, ⊥ is a component of proper acceleration in a direction perpendicular to the surface upon which the vehicle travels, ν is a speed of the vehicle along the ground, νi is a ground speed upon initiation of a test protocol segment, νƒ is a ground speed upon conclusion of the test protocol segment, m is a mass of the vehicle, hi is the height upon initiation of the test protocol segment, hƒ is the height upon conclusion of the test protocol segment, I is a net moment of inertia of tires on the vehicle, R is an average radius of the tires on the vehicle, g is acceleration of gravity, and Wother is work done by other dissipative forces on the vehicle.