Maximizing Toboggan Speed: Calculating Slope and Adjusting for Weight and Dips

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In summary: So if you're only interested in the change in kinetic energy, you could calculate it as follows:In summary, you will need a height change of 16.1 m to achieve 40 mph on a toboggan.
  • #1
zoltar
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i need help, i need to calculate the slope of a hill to reach 40mph on a toboggan? how do i do this with a fluctuating toboggan weight...meaning what is the slope i require for different weights? also how would i adjust for dips in the hill?

can anyone help? this is not might area and would appreciate something simple that i could use.

thanks!
 
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  • #2
Welcome to PF!

zoltar said:
i need help, i need to calculate the slope of a hill to reach 40mph on a toboggan? how do i do this with a fluctuating toboggan weight...meaning what is the slope i require for different weights?

Hi zoltar ! Welcome to PF! :smile:

Acceleration is what matters, and as Galileo proved (on a slope, by the way), all weights have the same acceleration under gravity.

So the weight doesn't matter. :smile:
also how would i adjust for dips in the hill?

Not following you … what sort of dips? :confused:
 
  • #3
It's not so simple.

It depends on the friction of the toboggan on the snow - which depends on the design of the toboggan, and the quality and temperature of the snow.

And then it also depends on the air resistance of the toboggan and its rider(s).

So there isn't a simple formula that will give the right answer. You're probably better conducting an empirical experiment (trying it out for real, and seeing what results you get).
 
  • #4
It is relatively simple if you assume no air resistance/friction etc. But it will depend on how much space you have and how quickly you want to reach your target speed.

[tex] \frac{1}{2}m (\Delta v)^{2} = mg \Delta h[/tex] (kinetic energy gained = gravitational potential energy lost)

[tex] \Delta h[/tex] [tex]= \frac{v^{2}}{2g}[/tex]


[tex] = \frac{(40*1.6)^{2}}{2*9.8} = 209m[/tex]

So you will need a height change of 209m to achieve 40mph. Now you can calculate, using right-angled-trigonometry and knowledge of the space available, the angles you'd need to achieve this. Note this is just an approximation of course.
 
  • #5
quark1005 said:
[tex] = \frac{(40*1.6)^{2}}{2*9.8} = 209m[/tex]

So you will need a height change of 209m to achieve 40mph. Now you can calculate, using right-angled-trigonometry and knowledge of the space available, the angles you'd need to achieve this. Note this is just an approximation of course.
One should be careful with units here. The numerator would have units if (km/hr)2 and the denominator units of m/s2, so one must apply conversion factors 3600 s/hr and 1000 m/km. In doing so, the above expression becomes,


[tex] = \frac{(40*1.6)^{2}}{2*9.8*3.6^2} = 209 / (3.6)^2 m = 16.1 m[/tex]


Also, the change in kinetic energy is proportional to [tex]\Delta(v^2)[/tex], not [tex](\Delta{v})^2[/tex].
 

FAQ: Maximizing Toboggan Speed: Calculating Slope and Adjusting for Weight and Dips

How can I increase the speed of my toboggan?

There are several factors that can affect the speed of a toboggan. One way to increase speed is to reduce the friction between the toboggan and the surface it is riding on. This can be achieved by using a wax or silicone spray on the bottom of the toboggan. Additionally, making sure the surface is smooth and free of debris can also help increase speed.

Does the weight of the rider affect the speed of a toboggan?

Yes, the weight of the rider can have an impact on the speed of a toboggan. A lighter rider will typically go faster than a heavier rider due to the effect of gravity. However, the slope and surface conditions also play a significant role in determining the speed of a toboggan.

Is there a recommended slope for tobogganing?

The ideal slope for tobogganing depends on various factors, such as the type of toboggan, the rider's experience level, and the desired speed. Generally, a slope with a gradual incline and a smooth surface is ideal for beginners, while steeper slopes can provide more speed for experienced riders. It is essential to choose a slope that is safe and appropriate for your skill level.

Can the shape or design of a toboggan affect its speed?

Yes, the shape and design of a toboggan can have a significant impact on its speed. Toboggans with a sleek and aerodynamic design will typically go faster than those with a bulkier design. Additionally, the weight distribution and material used in the construction of the toboggan can also influence its speed.

How can I slow down or stop a toboggan if I am going too fast?

If you find yourself going too fast on a toboggan, there are a few methods you can use to slow down or stop. One option is to drag your feet in the snow, which will create friction and slow down the toboggan. You can also use your hands to dig into the snow and create resistance. It is essential to practice these techniques in a safe and controlled environment to ensure your safety.

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