It's all already done and graphed here Carx which should save you some time and effort.

You can see from the graph that time dilation due to velocity is not noticeably consequent until the order of about half the speed of light. At that point the length of time gradually increases and is approaching double that of the inertial reference. At 70%-80% of lightspeed it has about reached double (ie 1 day for the inertial frame is 2 days for the moving body), but it is not until you get very close to the speed of light that the dilation of time begins to sharply increase and approach infinite. Between 90% and 100% of lightspeed the rate of change in time per unit of velocity becomes huge.

Thank you DG & Eloise  .
I always invented the well and I postulate a different approach in my mind to this
1) the speed of light in a vacuum is the fastest thing we know.
2) Electrons and other particles/forces move slower then the speed of light.
3) Imagine a infinite energy source and a engine that will convert this energy into movement in outer space (we have no friction)
4) lets fallow the path of electrons while they enter  the engine to generate movement , while we are increase the speed the electrons will move slower and slower to their goal at the engine because the engine is “running away from the electrons”.
5) if the  engine or the ship approached electron speed the addiction of more speed is impossible because the electrons will stand still and if we move faster they start “moving backwards “.
6) and so did I reason that you can not go at light speed.

Is my reasoning correct ?

The same is true with a gravitation frilled that "grabs" electrons and other particles/forces from interaction with  other particles/forces . And it creates something I named time freeze (solving down of time do to fast movement)  and the correct or absolute time is a stationary frame of reference (0 speed , 0 time freeze) because after a Q&A in relativity there is no relativity we have a absolute time frame and everything else can only slow down  the reactions like in a refrigerator that slows down chemical reactions (actually its even more easy to explain relativity that way without confusing a simple audience) , so the twin paradox is only a paradox for people who think there is a refrigerator paradox because one fruit/chemical reaction “ages” slower  in a refrigerator then the other fruits/chemical reaction  in room temperature.

 There is no (literary)relativity in (physical)relativity.
Everything is relative to the ultimate time frame (correct time) and this ultimate  time frame is the speed of light at its maximum (100% stationary frame) every deviation is simply slowing down do to time freeze.
 

Is my reasoning correct ?

Technically yes, but only trivially true as no material object capable of "percieving" time could travel at c.

It's a mind exercise, and I'm not so good at math.

Hypothetical surfer, capable at moving at or near c. Assume time is constant. What other factors could change?

Poor deludedgod, having to explain what should happen in impossible hypothetical situations to people who don't know enough about physics.

LIKE ME!

Would this surfer be crushed under his own mass and become a miniature black hole like those ones postulated by the LHC haters?

If he used LOTS of dapper dan hair pomenade, would he be able to maintain his original style throughout the trip?

Would the sleeves on his hawian shirt appear shorter from the perspective of the surfer, due to the lorentz contraction?

This reminds me of a Limerick penned by a clever wag:

There once was a fellow from Fisk

Whose fencing was exceedingly brisk

So fast was his action, that the Lorentz contraction

Turned his rapier into a disk

An object which is moving at close to c will tend to "shorten" in the direction of motion. Once we talk about what happens to the surfer however, we are going beyond the thought experiment. The surfer, of course, is a biological organism, who could not possibly survive the contraction. But, no, the surfer will not become a little black hole. 
 

Not relative to the rest of him, as the whole object is shortened in the direction of motion. This means if a resting observer viewed the surfer from behind, they would see no change, but if someone viewed the surfer from the side, they would see him contract. 

Do you mean 'reinvented the wheel', Carx? There's nothing wrong with that at all, it's good exercise for the mind. So let's see what you have-

Basically, but they are also able to move at speeds very close to c, within the ranges of extreme time dilation which you saw on that graph.

So do you mean the electrons are providing an electrical charge to your hypothetical engine?

So you are saying that the charge cannot reach the drive mechanism because the drive mechanism is moving away from the charge at a faster velocity?

I think your reasoning runs into a problem here because the charge would be carried along a conductor that forms part of the accelerated mass, so to the electronic charge the conductor is a stationary frame that it is running across. The conductor doesn't outrun the charge in this case.

On the other hand as your hypothetical vehicle approaches lightspeed it gains mass  and in order to accelerate it further you would have to increase the charge exponentially. This result would manifest physically in a similar way to what you're describing, the charge could not get to the drive mechanism fast enough to accelerate the vehicle and its speed would plateau just the same.

Well if the electron charge is required to jump a gap or tunnel a vacuum in the mass to get to the drive mechanism then that would make sense, but in the sense that the charge to the drive is conducted along a portion of the mass itself, no, the charge is 'attached' to the mass and is moving relative to it the whole time.

The electrons aren't travelling faster than light, they are travelling through the electrical system of the ship and engine in relation to the ship.

Think of a fly sitting on a car seat, with the car moving at 100 miles per hour. The fly isn't moving, the car is. If the fly takes off and flies toward the front of the car at 1 mph, it's relative to the car, not the ground

Ok, I can't help but be ask this, since we're on the subject.  DG, it's my understanding that standard motion (I'm not a physicist, never claimed to be.  Sorry if I'm getting any terminology wrong.) for lack of a better term, is limited by c, and because of Lorenz contraction, any attempt to move biological organisms anywhere close to c would result in the death of the organism.  Am I then correct in saying that moving linearly through space-time, near light speed travel is physically impossible for humans?

Now, addressing non-standard motion, what I'm talking about is the much touted idea of bending, folding, or otherwise manipulating space-time so as to allow one to traverse what would ordinarily be a staggering distance with almost no ordinary movement.  It's my understanding that the concept of a wormhole is highly theoretical, but that if it is possible, it would require energy on an order of magnitude approaching that of a significant astronomical event, perhaps a supernova.  Is this correct?

Regardless of the energy requirement to form a wormhole, am I correct in my understanding that there would be a phenomenon similar to an event horizon, and that a biological organism could not hope to pass through a wormhole alive?  (Assuming it was big enough for that to be possible, which seems unlikely to me, but then again, I'm not a physicist.)

Your last sentence makes no sense if the fly would be slower then the car it would not move forward. Its not appearing it is faster if its moving in the same vector like the car !  

If you calculate the difference between the speed of a car inside the car and the fly you will get the speed difference between the car and the fly and the same speed difference is true for you calculating it on a plain , on the ground , or in a tree. You simply think that a moving body somehow haze its own speed is wrong you simply calculate the speed difference between the fly and the car inside if you add the real sped measured with a laser gyroscope you will get the true speed of the car and the fly.

Your conception is write however you are measuring speed difference not actual speed inside a car the same speed difference is true if measured out side its speed difference of fly to car + the velocity of the car or use a laser gyroscope it uses light in a vacuum.

BTW :

In common usage, however, people may also use the term "inertia" to refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), and sometimes its momentum, depending on context (e.g. "this object has a lot of inertia&quot. The term "inertia" is more properly understood as a shorthand for "the principle of inertia" as described by Newton in Newton's First Law of Motion which, expressed simply, says: "An object that is not subject to any outside forces moves at a constant velocity, covering equal distances in equal times along a straight-line path." In even simpler terms, inertia means "A body in motion tends to remain in motion, a body at rest tends to remain at rest." On the surface of the Earth the nature of inertia is often masked by the effects of friction which brings moving objects to rest relatively quickly unless they are coasting on wheels, well lubricated or perhaps falling or going downhill, being accelerated by gravity. This is what misled classical theorists such as Aristotle who believed objects moved only so long as force was being applied to them.[2]

~From wikipedia

And Velocity is linked to speed you simply described the same concept like me not even knowing this .

I don't know. The effects of Relativity aren't very noticeable until nearly .9c. You can see from the Lorentz transforms that a tick of 1s in the stationary frame takes 1.4s at 0.7c, but will take 2.3 seconds at 0.9c. The same transforms apply to contraction. I actually don't know the answer as to what will happen to an object below those speeds.The Lorentz contraction can be computed by the same transform. It's very hard to conceptualize because the actual "object" is not compressed (which would kill an organism), but the space-time around the object contracts. An observer would therefore see a compressed object. But the actual object wouldn't notice. That's why I actually couldn't answer with complete confidence that an object at, say, 0.8c, wouldn't survive. At, say, 0.9999c it would be irrelevant since any spaceship would become a pancake.

That is momentum which is the velocity multiplied by the mass; a vector multiplied by a scalar so that momentum is basically an increase in the magnitude of the velocity vector given by the mass of the object. Because of that similarity between momentum and velocity it's not easy to discern them in a cursory observation. One intuitive way to look at the difference is to consider momentum as transferable kinetic energy of which velocity plays a part but is not itself transferable. ie the car does not transfer velocity to the person, it transfers momentum enough to propel the person at the same velocity.

Now the person in the car is propelled along at the velocity of the car and you can say this is because it is part of the car's mass in the instance that they are travelling along concurrently, they have the same velocity but they each carry their own momentum.

When the car brakes its momentum is transferred through the braking system as heat and sound and friction which tears away some of the brake lining. The person in the car does not transfer momentum energy via this process so that when the system velocity winds down during braking the human is carrying the energy of it's momentum and must transfer it somewhere the same way the car has done.

So basically the phenomenon is not due to the person travelling independently of the car but rather having a mass of left over energy due to the speed which must be discharged independently of the car. This momentum has been transferred by the car to the person and by doing so the car and the person have become unified as one system moving at velocity but the person cannot just hit a button to transfer that energy back to the car on braking. The human body has to use up the energy it has gained and the only practicable method from within the car is movement.

BTW The seat belts absorb the energy via elastic collision with the body.