Introduction
The performance characteristics and energy consumption of a proposed mechanical hybrid vehicle were investigated; the hybrid consisted of an internal combustion engine and a flywheel rotational energy storage device. Four operating modes were envisioned for the system: a start-up mode in which the flywheel would be brought to operational speed if it was not already at that speed, an acceleration mode in which the vehicle would be accelerated to cruising speed, a cruising mode in which the vehicle would travel at constant speed for a period of time, and a braking mode in which the vehicle would decelerate from cruising speed to a full stop and enter into an idling mode; in the braking mode, the vehicle would remain stationary for a period of time with the engine turned off, conserving fuel and significantly reducing atmospheric pollution. The vehicle then would reenter the acceleration mode, beginning a new cycle of accelerating, cruising, braking, and idling.

The purpose of the investigation was to determine whether the proposed vehicle would be competitive with, more energy-efficient than, and less polluting than a conventional vehicle driven only by an internal combustion engine. Improved energy efficiency of the hybrid would be achieved by storing energy in the flywheel while the vehicle was in a braking mode; in this mode, energy ordinarily is lost because of the generation of frictional heat in the braking system, as is the case with a conventional vehicle. Currently available electric-hybrid vehicles achieve similar efficiency improvements by using an internal combustion engine, electric motors for propulsion, and batteries for electrical storage.

Flywheel Mechanics
The flywheel selected for the mechanical hybrid vehicle considered in this investigation had minimal size and weight and a peak design rotational speed consistent with the maximum allowable tensile stress of the flywheel material. The resultant flywheel was 18 inches in diameter and 6 inches wide, fabricated of structural steel material, with a yield stress of 30,000 PSI, an ultimate tensile stress of 60,000 PSI, a weight of 442 pounds, a maximum rotational speed of  2100 RPM, a maximum tensile stress of 3050 PSI, and a resultant safety factor of 10:1, based on the yield stress. With this flywheel it was possible to accelerate the vehicle to 40 MPH in 10.5 seconds, with the flywheel rotational velocity decreasing from 2100 to 1000 RPM in the process.

The relationship between the rotational speed and maximum tensile stress of the flywheel was obtained as follows:

dF = (dW)fw(Vmax)²/(g)(R)
V = (RPM)max(Pi)(2)(R)/(60)
dW = 2(Pi)(R)(dR)(t)(Density)fw
dF = 8(Pi)³(R)²(dR)(t)(Density)fw(RPM)²/(3600)(g)

Combining the above and integrating yields the following:

Fmax = (8)(Pi)³(R)³(t)(Density)fw(RPMmax)²/(3)(3600)(g)                (1)
Smax = Fmax/(Dmax)(t)(144)                                                        (2)

Energy absorbed or recovered from the flywheel is obtained as follows:

dE = (dW)(V)²/(2)(g)
V = (RPM)(Pi)(D)/(60)
dW=(Pi)(D)(dD)(t)(Density)fw
dE = (t)(Density)fw(Pi)³(D)³(dD)(RPM)²/(2g)(3600)

Combining and integrating these equations gives the following net energy for a flywheel in which the initial rotational speed differs from the final rotational operating speed:

Efw = (t)(Density)fw(Pi)³((RPM)i)² – (RPM)f)² ))(D)4/(4)(2g)(3600)            (3)

Flywheel energy loss resulting from air friction is obtained as follows:

dE = (dF)(V)²/(2g)
V = (RPM)(2)(Pi)(R)/(60)
dF = (Cd)(V)²(2)(Pi)(R)(dR)(2))(Density)air/(2)(g)

Combining and integrating these equations yields the following:

Eaf = (Cd)(RPM)4((2)(Pi))5(R)6(2)(Density)air/(2g)² (60)4(6)                (4)

Flywheel power loss resulting from roller bearing friction is as follows:

Pbf = (Cf)(Wfw)(2)(Pi)(Rb)(RPM)                                                         (5)

Mechanical Hybrid Component Arrangement and Operating Modes
The schematic arrangement of the hybrid components and operating modes are shown in Figure 1. A description of the itemized components is given in Table 1.

Figure 1. Schematic Diagram of Components
and Operating Modes for Mechanical Hybrid

Table 1: Mechanical Hybrid Components

Item Number	Description
1	Friction clutch, hydraulically opened or closed by on-off solenoid valve.
2, 3, 4	Same as item 1
5	Structural steel flywheel, 18 inch outside diameter and 6 inches thick
6, 7	Flud torque converters
8	Multivariable transmission
9	25-horsepower internal combusion engine
10	Front wheels with friction braking, driven by engine or flywheel
11	Drive belts and sprockets
12	Unpowered rear wheels with friction breaking
13	Sequencing of the components for the varios operating modes controlles by a programmable logic controller

Comparative Energy Requirements for Mechanical Hybrid and Conventional Vehicles
Equations for determining energy requirements for charging, acceleration, cruising, and braking operating modes are as follows:

Charging:             See Equation 3
Acceleration: (Eacc) = – ((Wv)(Vv)²/(2)(g) + (Rv)(Lacc))       (6)
(Rv) = –(((Cv)(Vv)²(Density)air)(Av)/(2)(g)) + ((Cvr)(Wv)))    (7)
Cruising: (Ecruise) = –((HP)(33,000)(Tcruise) + (Rv)(Lcruise))  (8)
Braking: (Ebraking) = (–Eacc)  (9)

Calculated data based on these equations are given in Table 2

Table 2: Energy Requirements and Operating Data
(Measurements in Foot-Pounds)

	Mechanical Hybrid	Conventional
Operating Mode 1, charging	-186,500	0
Operation Mode 2, accelerating	-144,200	-111,400
Operating Mode 3, cruising	-825,000	-825,000
Operating Mode 4, braking	+144,200	-111,400
Net energy requirements exclusive of charging	-825,000 ft-lbs	-1,050,000 ft-lbs.

Summary
This article has shown that a conventional nonhybrid vehicle powered by a 25-HP internal combustion engine and weighing 1500 pounds is more fuel-efficient than a mechanical hybrid weighing 1,942 pounds inclusive of an energy storage flywheel weighing 442 pounds and powered by an internal combustion engine with the same horsepower. Thus, on a trip totaling 75 miles in which the vehicles brake to a stop every 5 minutes, after cruising at 40 MPH, the mileage per gallon of fuel is 49.6 MPG, based on a fuel heating value of 145,000 BTU per gallon and an engine efficiency of 25%, for the conventional vehicle compared with 39.4 MPG for the hybrid, which travels a total of 58 miles at the same cruising speed and the same time interval before braking; this is a miles per gallon difference of about 25% in favor of the conventional vehicle. On shorter trips totaling 12 miles for the hybrid and 16 miles for the nonhybrid in which the vehicles brake to a stop every minute, the miles per gallon figure  is only 8% greater for the conventional vehicle.

The lesser fuel efficiency of the hybrid is due in part to its greater weight and in part to the need for mechanical recharging of the flywheel before each trip if the vehicle has remained idle for a significant time interval before beginning a trip; the flywheel will lose its charge, with RPM decreasing from a maximum operating speed of 2100 to 0 RPM, in about 2 hours, mainly as a result of roller bearing friction. Recharging to maximum operating speed with the internal combustion engine would require 14 seconds.

Hybrid fuel efficiency could be improved somewhat by reducing flywheel weight and increasing operating speed. However, reducing the flywheel weight by a factor of 2 would require an increase in operating speed by a factor of 4 to 8000 RPM. This could prove hazardous, however, if the wheel fragments or breaks away from its drivetrain.

Nomenclature
Av = frontal cross-sectional area of vehicle, square feet
Cv = vehicle drag coefficient, unitless, = 1.0
Cvr = coefficient of wheel rolling friction, unitless = 0.03
Cd = flywheel air drag coefficient, unitless = 0.005
Cf = coefficient of flywheel roller bearing friction, unitless = 0.003
D = flywheel diameter, feet
Density = pounds per cubic foot
E = energy absorbed or released, foot-pounds
F = centrifugal force, pounds
g = acceleration of gravity, feet/(sec)²
HP = internal combustion engine horsepower, (foot-pounds)/minute
Lacc = vehicle travel distance during acceleration = 300 feet
Lcruise = vehicle travel distance during cruising, feet
MPG = fuel consumption, miles per gallon of fuel
MPH = miles per hour
Pbf = flywheel power loss resulting from air and bearing friction, foot-pounds/minute
R = flywheel radius, feet
Rb = outside radius of flywheel bearing, feet
Rv = vehicle linear resistance to motion, pounds
RPM = flywheel rotational speed, revolutions/minute
S = flywheel tensile stress, PSI
T = cruise time, minutes
t = flywheel thickness, feet
V = velocity, feet/ second
W = weight, pounds

Subscripts
i = initial
f = final
max = maximum
fw = flywheel
air = ambient surroundings
af = air friction
acc = acceleration mode
cruise = cruise mode
braking = braking mode
v = vehicle