$1.$ Data for a typical passenger car is listed in the following table.$$ Assume the car can reach a speed of $124$mph at maximum power in $5$th gear $($final$).$ Keeping the $5$th gear ratio, build the following:

a$.(10$ Points$)$ Estimate the Engine Power Curve based on the techniques shown in class.

b$.(5$ Points$)$ Generate the Road Load Equation

c$.(10$ Points$)$ Gears for a Geometric Gearbox Design

d$.(10$ Points$)$ Gears for a Progressive Gearbox Design based on the techniques shown in class

$$

Curb Weight

$4022$ lbs

Wheelbase

$106\mathrm{.}3$ in

Peak Power at $6000$ rpm

$242$ hp

Peak Toque at $4500$ rpm

$226$ ft$-$lbs

$5$th Gear Ratio

$\mathrm{.}73$

Final Drive Ratio

$3\mathrm{.}68$

Tires

P$235/70$R$16$

Frontal Area

$16\mathrm{.}75$ ft$^2$

Coefficient of Drag $[$CD$]$

$\mathrm{.}35$

G$$box Overall Efficiency

$\mathrm{.}85$

Shift Time Between Gears

$\mathrm{.}5$ seconds

Launch Time

$2\mathrm{.}50$ seconds $1.(35$ Points$)$ Data for a typical passenger car is listed in the following table. Assume the car can reach a speed of $124$ mph at maximum power in $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash )$ gear $($final$).$ Keeping the $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash )$ gear ratio, build the following:

a$.(10$ Points$)$ Estimate the Engine Power Curve based on the techniques shown in class.

b$.(5$ Points$)$ Generate the Road Load Equation

c$.(10$ Points$)$ Gears for a Geometric Gearbox Design

d$.(10$ Points$)$ Gears for a Progressive Gearbox Design based on the techniques shown in class

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|\}$

$\backslash$hline Curb Weight & $4022$ lbs $\backslash \backslash$

$\backslash$hline Wheelbase & $106\mathrm{.}3$ in $\backslash \backslash$

$\backslash$hline Peak Power at $6000$ rpm & $242$ hp $\backslash \backslash$

$\backslash$hline Peak Toque at $4500$ rpm & $\backslash (226\backslash$mathrm$\{$ft$\}-\backslash$mathrm$\{$lbs$\}\backslash )\backslash \backslash$

$\backslash$hline $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash )$ Gear Ratio & $\mathrm{.}73\backslash \backslash$

$\backslash$hline Final Drive Ratio & $3\mathrm{.}68\backslash \backslash$

$\backslash$hline Tires & P$235/70$R$16\backslash \backslash$

$\backslash$hline Frontal Area & $\backslash (16\mathrm{.}75\backslash$mathrm$\{$ft$\}\{\}^\{\backslash$wedge$\}2\backslash )\backslash \backslash$

$\backslash$hline Coefficient of Drag $[$C D $]$ & $\mathrm{.}35\backslash \backslash$

$\backslash$hline G'box Overall Efficiency & $\mathrm{.}85\backslash \backslash$

$\backslash$hline Shift Time Between Gears & $\mathrm{.}5$ seconds $\backslash \backslash$

$\backslash$hline Launch Time & $2\mathrm{.}50$ seconds $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$