Force required to break a tree

Firstly, my condolences/sympathy.

Secondly, it will be hard to give you an accurate number without more detailed information of the scene. Mainly, the biggest factor/unknown is the decelaration - it is significant to the final force calculation of the impact. On one extreme - the bike could have completely sheared the tree (decelarated a little) and continued on - the second extreme is the bike had just the right amount of energy to shear the tree and come to a final stop right at the trunk.

(note I don't even feel 'right' offering that much information to this tragic event - and after having typed this much I feel I might as well hit submit - but have now realized I am not going to respond any further - nor read this thread anymore)

I am going to assume that he had just enough energy to break the tree and stop, as this would lead me to a minimum velocity to accomplish this feat. It becomes far too cumbersome if we were to calculate things like distance traveled after he hit the tree, deformation of the motorcycle around the tree, etc - just looking for a ballpark. I know the bike (Kawasaki Ninja) has a top speed around 180 MPH, and the weight of the bike, himself and his passenger was somewhere in the neighborhood of 800 lbs. I have no way of knowing how much area of the tree he was in contact with prior to its breakage, so Im just looking for some general equations.

Thanks

Avery Montembeault

I'm am sorry for this tragedy, this may be cold just bare with.

Also time of the year when it happen, when type of evergreen Yellow pine is quite strong yet brittle as compare to white pine, as compared to balsam.

A motorcycle accident, its tough to call no matter how fast. It could be the position of his body, It really does not take much for internal injuries.

It may not have snapped off the tree yet still be a fatality, or if the body was poition it could have snapped off the tree and one could still walk away.

can not give you comfort for a conclusive answer.

sorry

phoenix911

They are all correct.

I calculated the minimum force on the weakest tree.

If my calculations are correct, a 150 lb object travelling at as little as 4 mph with a contact area about 4 square inches would have enough kinetic energy to overcome the mudulus of elasticity of a 6 inch white pine tree.

Guest No. 1 was on to it as he mentioned deceleration (F=ma, not F=va).

The deceleration is the rate of change in velocity over time, not the velocity. The velocity change should be instantaneous having units of -ft/sec/sec for example.

If for example, he was going 88 fps (60 mph) before impact, how fast was he going 0.01 seconds after impact. A very high number for deceleration means a very high force was applied to the tree. If the deceleration was much less, then the force on the tree was much less.

What is the "mudulus" of elasticity?

The tree may have failed in shear or in bending depending on the forces applied to it.

Hi, "Guest #1" here again -

I know I said I wouldn't comment, nor read this thread again - but here I am ........

Anyways, a little more help for you:

http://www.independencepolice.org/pdf/CrashScienceJuly06.pdf

I would suggest that the tree failed in shear and a guesstimate of the shear strength of the tree would be 750 psi.

You know the area of the tree (28.27 in²) therefore an approximate force would be:

750 lbs/in² X 28.27 in² = 21,203 lbs

I will leave it to you for the rest of the math - Note the deceleration time is significant to the problem.

Modulus of elasticity etc

I simply calculated the absolute minimum speed required, There are so many variables, such as knots, moisture, specific growth patterns, species, as well as everything else that was mentioned, etc, that all is only a wild guess. All changes to the variables will only increase the speed. Nobody can give an accurate answer without specific testing. Obviously not 100 % of the kinetic energy will be transferred instantly.

The point is the family will assume that he was speeding. My calculations prove that this may not be the case.

This is a great reference here

Good. You got the spelling right this time. Excellent!

Morbid!

BTW, did he hit it or the motorcycle?

Sorry for your loss. This whole discussion seems a little indelicate, but you seem curious about the physics behind such a thing and, to be honest, I can't blame you at all as I believe I would be wanting the same questions answered. I think those who have responded have given you a pretty reasonable estimate. However, as a physicist I have to make one comment. The change in velocity will absolutely not be instantaneous as one responder told you. The time required for the change in velocity will include the time during which the tree is being bent prior to its shearing off (which is the failure mode as mentioned) as well as the time during which the motorcycle is being damaged. This total time will be short, but is not zero.

The average force is equal to the change in momentum (final mass*velocity - initial mass*velocity) (negative sign indicates direction of force opposite to initial direction of travel) divided by the time over which that change in momentum occurs. However, this can only be used as a rule of thumb since by doing it this way we are averaging the force over the total time. As the motorcycle just barely touches the tree, the force is small, as it reaches the point where the tree has been stretched to its limit and the motorcycle has been dented to its limit, the force will be its greatest. As soon as the tree snaps, the force drops to zero. Basically, the force required to break the tree can be provided at a lower rate of speed than one would calculate using the average force calculation based on change of momentum and a reasonable impact time. To deal with this on a reasonable basis without having to resort to calculus, the tables you have been referred to have been tabulated. Again, they provide a reasonable and surprisingly accurate estimate.

age and health of the tree will matter a lot. we have had a drought across the USA for several years not some trees may be brittle except at the core.

Much less that people in general realize...especially for most six-inch-dia trees of any (except tropical hardwood) species, of any age and condition. It really only depends upon the momentum and hardness of the impacting "body."

A more appropriate (less cart-before-the-horse) phrasing of the question would have asked: What is the maximum motorcycle speed below which the tree would not have been snapped in two? Thence...the same maximum below which the rider might have survived?

The former of those two questions is one for which, within some tolerance level, a "ballpark-figure" answer is possible. The latter, like the OP question, is greatly more problematic; thus, cannot yield any credible singular answer.

The best answer is to let "RIP" apply to survivors as well as the departed.