Physics investigations on Stunts

[Alain il professore]

Demonstration: Using the "Subtile" Unit
Scenario
Imagine you are playing "Stunts" and need to navigate a course with various obstacles and jumps. Understanding distances in "Subtiles" can help you make precise maneuvers.
Step 1: Understanding the Units

1 Tile = 62.5 meters
1 Subtile = 6.25 meters (1 Tile divided by 10)

Step 2: Measuring Vehicle Length

Suppose your vehicle is approximately 6.25 meters long.
This means your vehicle is 1 Subtile long.

Step 3: Navigating Obstacles

You approach a jump and need to know the distance to the landing zone.
The distance to the landing zone is 18.75 meters.
Convert this distance to Subtiles:

So, the landing zone is 3 Subtiles away.

Step 4: Adjusting Speed

You need to adjust your speed to successfully land the jump.
Your current speed is 12.5 meters per second.
Convert this speed to Subtiles per tick (1 tick = 1/20 second):

Your speed is 0.1 Subtiles per tick.

Step 5: Successful Maneuver

Knowing the distance to the landing zone is 3 Subtiles and your speed is 0.1 Subtiles per tick, you can calculate the time needed to reach the landing zone:

Since there are 20 ticks in a second, 30 ticks equal 1.5 seconds.
You have 1.5 seconds to adjust your trajectory and successfully land the jump.

By using the "Subtile" unit, you can make precise calculations and adjustments, enhancing your gameplay experience in "Stunts."

[Matei]

Your message is off-topic, but anyway.

Knowing the distance to the landing zone is 3 Subtiles and your speed is 0.1 Subtiles per tick, you can calculate the time needed to reach the landing zone:

Doesn't work because the car in Stunts doesn't always move the same. Sometimes it goes straight up, sometimes it goes down faster. All the stuff that you propose is also not fun when playing with a game. However, try doing this with those calculations:

https://www.youtube.com/watch?v=MorjKK2fjxA

...or this:

https://www.youtube.com/watch?v=y9O-vxPD-Ek

[Matei]

So how small are the cars in Stunts?

Lancia, one of the shortest original cars, is 79 points long, which amounts to 15.8ft or 4.82m, surely much larger than the real car.

https://www.ultimatespecs.com/car-specs/Lancia/7660/Lancia-Delta-HF-Turbo.html

Length : 390.0 cm / 153.54 inches

4.82 / 3.9 = 1.2359, so the car was estimated to be 23.59% larger, therefore it's (4.82 / 1.947) / 3.9 = 63.5% of the size of the real car. The width of the road was overestimated to be 14.6 m instead of 7.5 m - 94.7% larger. The volume of the car is (63.5%)^3 = 25.6% of that of the real car. The other cars are probably also around there.

[Matei]

And about the speeds and the gravity. The speed to make a jump between 2 ramps is ~80 km/h in my game and ~100 mph shown by the indicator in Stunts (I tried with Corvette ZR1, I didn't check all the cars), which means 100 * 1.6 / 1.947 = 82.2 km/h, so about the same. When leaving the ramp at a low speed, the cars fall in ~2 seconds in both games, so the gravity is modelled well enough in Stunts.

[Matei]

This becomes complicated.

the car was estimated to be 23.59% larger, therefore

as Duplode wrote:

the game designers have done so because it looks better at low resolutions.

The cars in Stunts are 1:2 scale models and they are drawn larger to look better at low resolutions.

https://silodrome.com/ferrari-250-gt-california-child-car/

The car is powered by a 110cc air-cooled, four-stroke petrol engine producing approximately 7 bhp and it can reach a top speed of 29 mph or 46 km/h, though this can be limited to lower speeds for younger drivers.

Problem solved.

[Duplode]

On gravity, we can explore how the jump behaviour fits (or doesn't) everything else by modelling a gap-jump as gravity-driven parabolic motion from the end of one ramp to the end of the other. The relevant equation is:

v = sqrt(2*d*g/sin(2*a))

Where v is the minimum speed to make it to the other side, d is half the length of a tile (the horizontal distance to the highest point in the flight), g is the acceleration of gravity, and a is the ramp angle.

For SimCarStunts, d = 16 m, g = 9.807 m/s^2 (the standard gravity) and a = arctan(450/1024). Therefore, v = 20.64 m/s = 74.30 km/h, which looks just right (I presume that accounting for the car having nonzero size would give us the ~80 km/h value seen in-game).

To allow for the toy world theory, we can also add a scale factor s which multiplies both v and d (but, importantly, not g), so that:

v = sqrt(2*d*g/(s*sin(2*a)))

We can now plug in our assumptions about the Stunts world and solve the equation for any variable we like.

For the approach I described earlier, which takes the speeds reported in-game as reference, we might set s = 1, d = 31.21 m and v = 100 mph = 44.69 m/s (taking 100 mph as a typical minimum speed for a Stunts car). Solving for g gives 23.57 m/s^2, fitting the picture outlined in the first post of this thread: very tall ramps for aesthetic reasons, with pseudo-gravity made strong enough to compensate.

Alternatively, we can keep d and v as before, set g to the standard gravity, and solve for the scale factor. That results in s = 0.4160 -- a toy world somewhat smaller than 1:2.

Yet another perspective is offered by setting s = 1 and g = 9.807 m/s^2, and then solving for a. That allows us to gauge how oversized Stunts ramps are. We end up with a = 0.1557 = 8.923°, which would correspond to a ramp height of 9.801 m, or 160.7 Stressed units -- slightly over a third of the actual height of the 3D model of the ramp, and very close to the height of the 3D model of the gas station.

[Matei]

I presume that accounting for the car having nonzero size would give us the ~80 km/h value

There's also the air resistance.

To allow for the toy world theory,

Only the cars are 1:2 scale model cars. The buildings and the road are obviously not at that scale. Besides, has anyone ever made a model world of 1 km²? And I already showed that:

When leaving the ramp at a low speed, the cars fall in ~2 seconds in both games, so the gravity is modelled well enough in Stunts.

So s has no place in the equation.

[Matei]

Falling, ramp height.

In my game (video attached): t = 6.5 - 4.8 = 1.7 s

In Stunts (images attached): t = 22 - 20.15 = 1.85 s

Ramp height h = g * t² / 2, ignoring the air drag.

Simcar: h = 9.81 * 1.7² / 2 = 14.17 m

Stunts: h = 9.81 * 1.85² = 16.79 m

The ramp is 14 meters high, so apparently the air drag is slightly larger in Stunts, probably because the models at 1:2 scale are lighter. We can observe that in Stunts the cars have much smoother landings.

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[Duplode]

I presume that accounting for the car having nonzero size would give us the ~80 km/h value

There's also the air resistance.

Indeed -- starting from 80 km/h, air drag slows down car 4 by about 4 km/h over a tile, so it's a meaningful effect for that kind of difference. (That's already discounting rolling resistance, which unlike in Stunts applies on roads.)