Sorry, but you are wrong... Physics dictate that you CANNOT get more energy from an object than you put into an object.. The only energy put into the train is the chain lift.. There are no other lifts that move the inert train.. Momentum is constantly degrading for the entire course of the attraction.. the ONLY exception is if the coaster was able to drop BELOW the level of the original climb.. In other words, if the coaster is lifted to 100 feet, drops 25 , helixes, and then drops another 125 feet because the grade of the land changes, then it would get additional energy.. but thats it... Sorry, but thats a proven fact in the world of physics.. And if you can show otherwise, there are many energy companies that would love to talk to you... .You can only get out of the train, what you put into it.. Thats it... So the energy in the train is at it's maximum after the first drop.. It erodes after that, without fail.
and btw, Energy Dictates Speed while coupled with grade.. Simple equation... Max speed is achieved ONLY when you spend the initial load of energy put into the train (for example: the large drop on everest for example spends the greatest percentage of the energy gained on the main lift climb)
No offence, but if you're going to basically shout at people with capitals and tell them that they are wrong you need to make sure you are correct yourself, which you aren't. You generally have the right idea but you are mixing up all sorts of physics and telling them to other people as if you are an expert.
First of all saying the energy in the train is maximum at the end of the first drop, incorrect. The energy in the train is at its greatest at the highest point of the roller coaster when there are no devices which add speed such as the magnetic launchers. The maximum energy that can be obtained from the roller coaster is the gravitiational energy between the highest and the lowest point, and the same applies for the maximum about of energy extracted on any drop, the top of the drop and the bottom. Obviously you will never get the total amount of energy from the system due to loss of energy from the system in the form of heat and sound. The only accelerating force is gravity, the only resistances are wind and friction.
Your statement about the momentum of the train constantly degrading is completely false, it is constantly rising and falling. Momentum is mass * Velocity, so at the top of the hill and loop it is virtually zero, and at the bottom of the hills at its greatest, so constantly degrading is incorrect.
Also energy is not 'spent' as it can be neither created or destroyed. When considering the energy of the train only, the only energy lost from that system is due to conversion of sound and heat energy from kinetic energy, but in terms of the overall energy of the train, only a small amount is converted to these other forms when operating on a low friction track with reasonable aerodynamics on the train.
Some people also seem to be mixing up the grade of the descent with the maximum speed available. Well, this is technically true but people seem to be mixing up the reason why. Unless i am getting confused with the vocabulary of different nations here, i am assuming the word grade here is in reference to the slope of the track, so 90 degrees grade would be a vertical drop, and 10 degrees grade a very shallow slope. Now, in a frictionless environment, it doesnt matter what grade you are on, if the change of height is the same, the speed at the bottom of the slope will be the same as acceleration is due to gravity only. for small differences in grade in a real environment, if the change in height is the same then the speed will be very similar at the bottom of the slopes as the difference in energy converted to heat due to friction will not be so great.
Now in terms of this discussion on the train rolling back and not making it up the hill, it doesnt make a whole great deal whether the train is full or not.
The total gravitational energy that can be used is mass * gravitational constant * height, converted into kinetic energy is 1/2 * mass * velocity * velocity, since the mass of the train doesn't change, unless someone throws up or something, then the velocity is basically independent of the mass of the train, regardless of it being full or not. The only real effect is there will be a difference of the friction on the track. There is not a great deal of tolerance in the conversion between the gravitational and kinetic energy built into the system, it could be worse if the coaster went too quickly over the top of a hill due to stresses on the train and riders than it rolling back.
Apologies if i have made any mistakes in my physics writing this, done this quite quickly.
