SOLAR CAR PROJECT MESSHIA YOUNG

ENGN 0040

MAY 7TH, 2013

 

EXECUTIVE SUMMARY 

PURPOSE 

The purpose of this report is to explain the calculation process and design process that fueled the development of the solar car. The primary objective for this project was to design and construct a small solar powered vehicle that possessed the ability to climb a ramp at maximum speed. So, for this project, it was necessary to specifically consider the design of the transmission and wheels, the weight of the car, the overall friction experienced by the car, and the placement of the solar panels.

OUTLINE   

This report contains an explanation of design calculations and design specifications. First, design calculations are discussed in detail. For accurate construction of our solar car, the relationship between voltage and current generated for the solar panels had to be calculated, as well as the relationship between motor speed and output power. In addition, we also calculated expected linear velocity, gear ratios and wheel radii depending upon angles of incline. Finally, this report outlines the overall design parameters and performance of the constructed solar car.

CONCLUSION 

In conclusion, we discovered that good design is important if one wants calculations to be applicable to the constructed solar car. Overall, we discovered that a wheel radius of 3.7cm was best for an incline of 15º and a wheel radius of 5.7cm was best for an incline of 10º. These combinations gave velocities of 0.204m/s and 0.360m/s, respectively. We found that this confirmed our predictions based on V=Pmotor/mgsin(incline_theta*pi/180). So, we found that our design calculations were very beneficial to our design process.

DESIGN CALCULATIONS  

Calculations were very necessary to ensuring the efficiency of our design.

SOLAR PANEL CHARACTERISTICS 

First, we determined the relationship between solar panels and the current generated by the solar panels. We started by plotting data given to us that related voltage to current in excel. In addition, the equation I=I0-I1(e

qV/nkT -1) was given to determine the current generated by the given solar panels. For this equation, “I” represents current, “I0” is the current generated by the photovoltaic effect, I1 is the reverse saturation current, “n” represents a constant that depends on the photovoltaic cells, “q” the charge of an electron, “V” is the voltage across the cell, “k” is Boltzmann’s constant, and “T” represents temperature in Kelvins. “I” was a given value in Amperes(A), I1=30µA, q=1.609*10-19 Coulombs(C), “V” was voltage given in the experimental data, k=1.38*10-23 J/K, T=353K.

Since everything for this equation was known but I0 and n, we made intelligent guesses as to the value of I0 and n, and then experimented with the data in excel until an I0 and n combination was achieved that

 

closely matched the data. We decided that I0=258V and n=13.7, these values gave the closest correlation to the experimental data while avoiding overshooting errors.

ELECTRIC (DC) MOTOR CHARACTERISTICS 

Then, given the conclusions of that analysis, the values of certain constants had to be determined using the experimental data provided to us. The electric current was related to voltage and angular speed of the motor by I=(V-βω)/R, where I is the current, V is voltage, β is a constant that depends on the motor configuration, ω is angular speed of the motor in radians/second, R is electrical resistance. The moment exerted by the output shaft of the motor was defined by this set of equations:

T=β -T0-τ0ω I>T0/β 1 I<T0/β

Where T0 and τ0 are constants that account for output losses due to friction, eddy currents, and air resistance. Upon solving this system of equations, we discovered that R=1.071 Ω, β=0.001728, T0=3.756*10-5 and τ0=3.103*10-7 .

RELATIONSHIP BETWEEN MOTOR SPEED AND POWER 

After that, we determined ideal motor speed to optimize output of the motor(power). We used excel to aid in visualizing this relationship. Given that ω=(-IR+V)/β and that I=I0-I1(e

qV/nkT -1) could be used to find Current (A) at given Voltages (V) and Torque= βI-T0-τ0ω, we plotted the data in an excel spreadsheet to discover which motor speed correlated to the optimum output wattage. Since power output of an electric motor is Torque multiplied by angular velocity, finding output in Watts for the motor at various voltages was very simple. To more easily visualize this data, we plotted motor speed (rad/sec) against motor output (Watts). We discovered that a motor speed of 1128.03 radians/second provided the highest possible power of 1.29 Watts.

Using this data, we found a slope related definition for velocity, V=Pmotor/mgsin(incline_angle*π/180) (in radians), we assumed that around 80% of motor output would be lost, so we scaled Pmotor down by multiplying it by 0.2. Given this relationship, we concluded that a linear speed for our solar vehicle was V=1.292*.2/.465*9.8*sin(15*π/180)=0.219 m/s. This data also confirmed that at a 15º incline, the gear ratio needed to be 1/256.

IDEAL GEAR RATIOS 

After determining what an ideal velocity would be, we then determined what gear ratio we needed. We found that a gear ratio of 1/256 was needed, which means we needed 4 gears. Each gear reduces motor output by a factor of 4, so this is why we needed four gears. So, by using 4 gears, the axle angular velocity was taken down to 5.97 radians/second which provide a car velocity of 0.219 m/s. In this way, our output would be closest to what we found to be ideal in terms of velocity that maximizes output.

OPTIMIZED WHEEL SIZE 

After that, we determined optimum wheel size. Since the relationship between linear velocity of the car and wheel radius “r” (m) and angular speed of the axle was given by V*=rω*. V* stands for linear velocity while ω* represents angular velocity of the axle in radians/second. So, r=V*/ω*. Using this relationship, we found that for an angle of 15º, the best wheel radius would be approximately 0.037 m. With the same

 

gear ratio of 1/256, at an angle of 10º we would need a wheel radius of approximately 0.055 m, while for 5º, the predicted wheel radius was 0.11 m.

DESIGN SPECIFICATIONS 

The total weight of our vehicle is 465 g. We decided to use three wheels, rather than four to reduce friction by 25%. In addition, our vehicle employs back-wheel drive because this was found to be more efficient than having the motor move the front wheels. Our car is 21 cm long and has solar panel supports that extend 20 cm from the ground. This allows for the attached solar panels to absorb as much artificial sunlight as possible. In addition, the gear ratio is 1/256, so we used 4 gears. This supplied the needed angular velocity to maximize output power. When we tested our vehicle, we found that overall, our calculations were rather accurate.

TESTING CONCLUSIONS 

We tested and calibrated our vehicle for 10º and 15º. For these inclines, back wheel radii of 5.7 and 3.7cm were used, respectively. The front wheel does not change and has radius 2.5 cm. We tested 5 runs each for each angle of incline. For 10º, the average velocity of the car was 0.360 m/s. For 15º. The average velocity was 0.204 m/s.