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On a 1% gradient (1 in 100) a locomotive can pull half (or less) of the load that it can pull on level track. In order for a bike to go up an incline at a constant speed, the net force must be zero (zero vector). It says that the frictional force is proportional to the force the surface pushes back perpendicular to the surface (we call this the normal force).I want to use this model for friction to solve for the maximum angle before this thing slides.I just need the coefficient of friction for a tire and a road interacting. 947 views. I would go for a speed of 2 m/s with a maximum power of maybe 300 watts. Ignoring San Francisco, I can think of a 10% grade on a highway pass (Jackson Hole, WY) and 6% is common on interstates in CO. But how long does it take to go up this incline? Really, the friction problem might be worse than this. It would actually be even higher. Suppose the bike plus rider has a mass of 75 kg with an average speed of 2 m/s. The bike only uses the back wheel for moving forward, so it is the friction on the back wheel that matters.

This angle is the sum of the slope angle (I will call θ) and the angle of the center of mass with respect to the wheels (which I will call α). Of course if the road is wet, this would go down to a coefficient maybe as low as 0.45. I'm not going to re-derive this center of mass stuff - if you want more details, check out Here is a diagram of a biker going up a hill. It seems trying to find one location for all road information isn't that easy.

Just go to the ReservationsEZ is a simple to use hotel finder that is not only easy to navigate but guarantees you to find the lowest rates. I would love to see the data this is based on (hopefully it wasn't just sketched up on a bar napkin during a heated discussion). The maximum gradient of local roads is usually restricted by local ordinance and will be on the order of 12% to 15% slope. If the biker is leaning forward, the weight distribution might not be even on the two wheels. Six degrees or less sounds much more advisable, like imperatively. I might be wrong though.For a bike going up an incline, the center of mass has be horizontally in between the two support forces. That is my fault.

Surely you know I don't really report on the news. Find out where the Steep Grades are before you get there, this directory is a must for exciting and a really fun adventure, but it also can be a dangerous venture.

Probably about 12.5 degrees is the steepest consistently workable in any context, say for a short entrance ramp at the end of a hill that needs to be high for some reason. Steep grades on the Interstates and Highways have been known to take many lives and cause severe accidents.

So, my estimate doesn't seem so crazy.Let me go ahead and say that I suspect the power limit above is going to be lower than the next two limits to the slope. I think this is a little much. It's possible, but it would wear you out quickly.

I really didn't know what I wanted to draw until I started drawing it. I think there are three reasons why a slope would be too steep. 148), which says: "The slope of the grade between two adjacent Vertical Points of Intersection (VPI), typically expressed in percentage form as the vertical rise or… Here I have labeled If the red dot for the center of mass is to the left of the blue dot for the back wheel, the bike will tip over. That's some serious power. If I measured the angle of the line from back wheel to center of mass, the angle of this line must be less than 90°. Where is the most dangerous road ever? We usually represent the steepness of a slope with an angle, but this essentially does the same thing. What does a 30% grade mean? If you want more details about the actual race, check out Now for the physics. In this case the support forces are the contact forces on the two tires. Looking at the triangle I added, I can find α.For the maximum slope, the sum of these angles would be 90°.Bikes can be different sizes, so let me just guess that A bike is more complicated than a solid block.

He said that on a 40k ride, he averages 280 Watts. Early railways in the United Kingdom were laid out with very gentle gradients, such as 0.05% (1 in 2000), because the early locomotives (an… I included a calculation to determine the angle from the gradient.Let's just put in some values here. Ffordd Penlech, Wales is the steepest road in the UK, with an average gradient of 20% and a maximum gradient of 40%. a 28.5m rise over the 100m) is way too steep unless the owner has a Hummer, or a winch and steel cable located at the top of the slope.

Eldred Street, Los Angeles, Calif.; 33 percent gradient. Steep grades on the Interstates and Highways have been known to take many lives and cause severe accidents. If the grade was 30, this would require a power of 441 Watts 422 Watts. I don't have a good feel for the power of a cyclist, but I asked my brother who rides quite a bit. For all of these cases, I am going to assume that it is a prolonged slope.