Dealing with Bacon (Deluxe)
By Zimo Wang, 27th Aug 2021
Translated by Zimo Wang, 2nd Nov 2023
Preface
The article will commence with an analysis of the pan and bacon. Step by step, we delve into the trajectory of the bacon. Some sections include force analysis diagrams, while others incorporate formulas. If you don't comprehend these formulas and images, don't worry. The blue sentences in the article represent conclusions that you can directly use.
Since this game accompanied me for half of a summer vacation, I analyzed its internal mechanics. Therefore, the article lacks any external references. All the data has been hand-measured, and the content is the product of my own conceptualization of the results. If you notice any issues, please bring them to my attention. I hope you enjoy it!
Summer vacation free time is not boring because of Bacon. The screen has a pot, followed by a bacon being thrown down. The player needs to combine his superb pan-turning skills to fling the bacon onto another object. The game is full of ideas that will blow your mind, but its own graphics are minimalistic. The game can only be found on IOS at the moment, but this is an article for everyone to read. Gameplay video:
PART 1: The Pan and Bacon
If you have played the game, you will know that clicking on the screen can make the pot tip; long press the screen to make the pot lift; not clicking makes the pot fall. After a one-to-one measurement with the screen, the pot is raised at an angle of 4° with the screen, and lowered at an angle of 12° with the screen, as shown in Figure 1:
Figure 1-The angle between the pan raised and the pan lowered from the horizontal
As you can tell if you've played the game, the bacon doesn't stay on the pan - it either slides to the left or to the right. This provokes me to think deeply about the pan and the bacon: it's quite a lot of oil (and really doesn't stick to the pan). But aside from the reason for oil, the reason it will slide has to do with friction. The friction of an object sliding is given by the formula F = μN, where μ is the kinetic friction factor, a constant, determined jointly by the nature of object 1 and object 2; N is the normal force. If horizontal, the positive pressure is equal to the force of gravity on the object (in the absence of an external force); in the case of the Bacon game, where the pan is at an angle to the horizontal, the normal force needs to be calculated by vectorial decomposition. For Bacon when the pan is lifted, a force diagram can be drawn.
Figure 2-Schematic of bacon force when the pan is lifted (not to scale)
In this case, bacon receives a total of three forces: the force of gravity W, the force of sliding friction f, and the force of support given to it by the pan N. Next, you can vectorially decompose bacon's force of weight into forces parallel to the pan and forces perpendicular to the pan.
Figure 3-Decomposition of weight
Well, you can see from this that the proportions in Figure 2 are indeed not quite right. Since gravity breaks down the vector that is parallel to the surface of the pan to be significantly less than the friction in Figure 2, if this were actually the case, the meat would have to slide to the right side of the pan. So improve Figure 2.
Figure 4-Standard schematic for bacon force when the pan is lifted
Figure 4 is a standard schematic diagram. In the diagram, the force of weight W is decomposed into W1 and W2, where W2 is horizontal to the pan and has a mode greater than the mode of the sliding friction force, meaning that the bacon ends up sliding to the left. W1 is perpendicular to the surface of the pan and has a mode equal to the mode of the supporting force N, making it a balanced pair of forces. Since the angle between the surface of the pan and the horizontal has been measured to be 4°, the magnitudes of W1 and W2 can be calculated, as labeled in the figure. So this means that the supporting force N = W1 = Wcos4°. The next two forces to be investigated are the two forces that are horizontal to the surface of the pan. This can be obtained from Newton's second law:
where m is the mass of bacon, but we don't know its mass. g is the strength of the gravity field, which is 10 on Earth, but we also don't know what the game is set to. So the symbols are kept. The only thing we can know is “a”, the acceleration.
How do you measure it? Anyway, I took a ruler and raked it over the iPad for ages to measure the distance, then recorded the screen to measure the time over and over again. We want to measure the distance the bacon slides across the pan and the corresponding time.
Figure 5-Recording Distance Measurement Time
At the moment the bacon is lying flat on the pan, measure its distance from the drop position, which is the distance it will slide. Then time it and wait until the bacon slides to the position at the head of the pan and press pause. Since human reaction time is involved here, I measured the time five times. The results are 1.29s, 1.37s, 1.29s, 1.44s, 1.45s, where the mean value is 1.368s. The distance moved ended up measuring 0.55cm, which is the distance on the screen. Let's use this data for the next calculations. Substituting the result into the following formula, we can roughly estimate the initial speed as 0, based on the gif:
This formula is subsequently applied to the formula derived earlier.
Since the formula has only two variables, it is then possible to draw a graph of the functional relationship. You can try to substitute g for any value larger than 1 and find that μ is always between 0.06-0.07. Therefore the coefficient of friction is about 0.07.
PART 2: How to Tip the Pan?
2.1 Is a long press beneficial?
When playing tennis or soccer or any other sport, a person will try to hit the ball as long as possible, which is why there is a swinging leg for shooting and a follow-through swing for tennis. This is because impulse I = Ft and impulse = change in momentum. If a ball is initially stationary, it means that extending the time of touch brings greater momentum, which increases the speed of the ball.
So for Bacon, theoretically increasing the contact time when upsetting the pot could also make Bacon run further. So we can do an experiment to prove this conclusion is correct.
First, measure the angle between the highest point at which the pan lifts up and the plane after touching the screen. Subsequently, measure at what angle the bacon leaves the surface of the pan. If the latter angle is greater than the former, then it can be obtained that the long press can be turned farther.
However, the angle at which the pan lifts up at the touch of the screen is also different. But at the moment thatthe bacon leaves the pan surface, the pan and the horizontal angle is 4 °, that is to say, as long as the light touch screen, the pan can be lifted to 4 °, then the speed of the bacon is the same, and then lifted up on the bacon does not have any impulse to change. But if the touch is too short and doesn't reach 4°, then it reduces its speed (a bit difficult).
Figure 6-The bacon leaves the instant pan at an angle to a horizontal plane
So, as long as the light touch is not too short and the pan surface is raised to an angle of 4° from horizontal, the distance of the bacon will not be affected.
2.2 Is it possible to "double jump"?
In this case, a double-jump means double-tapping the screen twice so as to apply force to the bacon once again after tipping the pan. That means touching the bacon twice in a row. Reading this you may have rushed to open the game and try to see if you can make the double jump. Next, we'll do the derivation and finally compare the times. Before that you can try to see if you can make a successful double jump!
First we calculate the speed of the bacon the moment it leaves the surface of the pan, this can be done using the following formula:
This formula is used for uniformly accelerated motion. Here we need to assume that the bacon was initially at rest on the surface of the pan and then thrown (ideal case), so the initial velocity u in the formula is 0. Also, v here represents the terminal velocity at the moment of leaving the surface of the pan, not the average velocity in bacon acceleration. Because the rotation of the pan is not linear, and the displacement d is linear here, it cannot be calculated directly. The linear displacement can be related to the angular displacement using the formula d=θr defined by the angular displacement, with r representing the radius, which is the distance between the pivot point of the pan and the bacon. So the equation becomes:
First theta units radians, which can be directly converted to angles. From our previous measurements, we can see that the pan is 12° to the horizontal when not touching a flat surface (Fig. 1), and the pan is 4° to the bacon at the moment the bacon leaves the surface of the pan (Fig. 6), giving an angle difference of 8°, which is calculated to be equal to 2π/45 rad.
And r is the radius. First measure the length from the pivot point of the pan to the bottom of the pan, i.e., the sum of the length of the pan's surface and the pan's handle. And note here that what we call bacon is measured as a point of mass, which is where its center of gravity is located. If we take the center of gravity to the bottom of the pan as the true r-value, half of the bacon would be outside the pan at this point. So in order to simulate a more realistic scenario, this r-value is cut in half of the length of the bacon (Figure 7). The final result gives 3.25cm - 0.65cm = 2.6cm.
Figure 7-The bacon leaves the instant pan at an angle to a horizontal plane
And finally t, time. But because t is so short here, the timer doesn't work well. I ended up rewinding the video to my computer, taking my editing software, and finding the moment in frames when the pan was about to be lifted and the moment when the bacon had left, recording the time and figuring out the difference. The final result is: 2.15435s - 2.13230s = 0.02205s.
Substituting the three figures into the formula then gives the speed v of the bacon at the moment it leaves the pan.
This velocity is the velocity of the bacon leaving the pan at an angle perpendicular to the surface. We want to know the velocity of the bacon vertically upwards at this point, so perform a vector decomposition. The vertical speed is cos4° x 0.3293m/s = 0.3285m/s = 32.85cm/s. So the vertical speed of the bacon the moment it leaves the pan is 32.85cm/s.
So, if double jump are to be successful, the speed at which the pan is tipped and dropped must keep up with the speed at which the bacon leaves the pan. The difference in height between the pan at 4° to the horizontal (the moment the bacon leaves the pan) and the bottom of the pan when the pan is fully raised is measured to be 0.9cm (Figure 8).
Figure 8-Difference in height between the highest point of the pot and the first jump in double jump
In the first jump, the bacon leaves the surface of the pan when the pan is turned for the first time. In the second jump, the highest height the pan can reach is 0.9cm from the first jump; if the pan does not have time to touch the bacon in the 9cm, the pan can not go up again, and we will watch the bacon fly away, and the double jump fails. The vertical speed of the bacon is 32.85cm/s. Using 0.9 ÷ 32.85 is 0.0274s, which means that the condition for the second jump is that you have to tap the screen twice in 0.0274s or less. This is very difficult, at least for me.
If you manage to do it, sorry, the game doesn't recognize that you tapped twice because the time difference is too short. It will just treat it as if you tapped once.
CONCLUSION: Double jump is not possible. First, you need to tap the screen twice within 0.0274s time interval. If you succeed, the screen won't recognize the two clicks and will only count them as one click.
PART 3: Bacon Tracks
After talking about the technique of tipping the pan, let's see the trajectory of the bacon. When talking about the trajectory of the bacon, the position of the bacon on the pan also needs to be taken into account, so the knowledge of the tipped pan will still be covered here.
First of all, in the case of levels where the target object is very small, it is necessary to draw a trajectory (parabola) before the pan is tipped, and then make the bacon move as much as possible in accordance with the pre-determined parabola, so as to increase the efficiency of passing the level. Let's take level 132, Peanuts, as an example to see how to set up a parabola.
Figure 9-Level 132: Peanuts
The target for this level is small in size, a peanut that is smaller than the length of the bacon. The best way to do this is to place the bacon's center of gravity point at the highest point to the left of the peanut (as shown in Figure 9). So the next step is to develop an ideal parabola. But how to formulate it? There are an infinite number of parabolas when giving only one point.
So before that, we need to know some relationship between the position of the bacon on the pan and the distance traveled. Playing with seesaws in everyday life we can all notice that when you sit on the head of a seesaw you can easily fly if another person applies a force to you across the pivot point (you have to be light enough and the applied force has to be high enough). But if you sit on the seesaw near the fulcrum, the same force will not cause you to fly. The exact description is shown in Figure 10.
Figure 10-The see-saw problem
It probably doesn't happen in everyday life, but that's how it plays out in cartoons.
So by analogy in this way, in the bacon game, bacon is more likely to fly high at the point furthest from the handle of the pan. So next compare the bacon at the two points in Figure 11. P1 and P2 represent the center of gravity of the bacon, and R1 and R2 represent its distance from the pivot point.
Figure 11-Two positions of bacon on the pan
And for these two different positions of bacon, they both had energy changes during lifting:
where θ represents the angular displacement, R represents the radius, and v represents the velocity of the bacon leaving the pan. As in the previous issue, we can't get this directly for the linear displacement, we need to get it in radians multiplied by the radius. The final result of this equation is the energy change of the bacon after accelerating from 0 speed during the process of inverting the pan. This energy change has mainly mechanical energy, being kinetic and potential energy. The change in potential energy is negligible and can be ≈ 0. So this formula gives us the change in kinetic energy.
Then come and compare why the bacon at the two points P1P2 in Figure 3 ended up flying different distances and heights. Obviously, they have different R. Since R1 is less than R2 (nearly double), the final change in ability will be quite a bit different. The final speeds are different because of the kinetic energy equation E=1/2mv^2. But the question here is, are θ and t the same for both P1 and P2 in the company? Not really, but it depends on how it is set up in the game.
This can be done by taking an everyday object and doing an experiment. I take a ruler (30cm long) and place two items with the same mass at 20cm and 30cm (I take a clamp). Hold the ruler horizontally in your hand at 0cm. The ruler is then given a quick spin to see which clip leaves the surface of the ruler first. If the description is not clear, see the gif below:
Figure 12-Test whether the same mass item t in different locations is the same
So you can see that when the ruler is rotated around the hand, the green clip leaves the surface of the ruler before the yellow clip (look carefully at the gif and take a screenshot if necessary for observation). And we can compare the ruler of this experiment to a pan, the green clip to the bacon at position P2, and the yellow clip to the bacon at position P1. So the experiment proves that t and θ are different for both P1 and P2 bacon.
Once the relationship is obtained, let's look at the fact that because the difference in time for the clip to leave the ruler surface is very short, we can estimate the difference between t and θ as 0. If you don't think that's accurate, then interpret it another way. See that the numerator and denominator are θ and t. Dividing two values that grow (rise similarly) at the same time changes the equation little. The change must be there because the angular velocity keeps increasing. On top of that, the degree of t at the denominator is 3. R2 is also significantly larger than R1.
To summarize, the change in energy at position P2 is significantly greater than the change in energy at position P1, thus explaining why Bacon, who is close to the fulcrum, cannot fly very far.
Next move the idea back to the parabola. The method of setting a parabola needs to be approached based on experience, and after playing around with it a lot you will probably have a range. Follow two rules when setting a parabola:
1. Don't set the apex of the parabola too high - flush with the target point or a centimeter above it will do.
2. Where the bacon leaves the pan needs to be in the front half of the pan (as in Figure 13).
Figure 13-Position of the bacon on the pan when tipping the pan
The first point of the two-point principle gives out the location of the highest point of the quadratic function. So in combination with the landing point given at the very beginning (Figure 9), a quadratic image can be made, which is the trajectory that Bacon took.
Figure 14-Bacon's Trajectory (Quadratic Function)
I like to locate the end point at (0, 0), so feel free. Subsequently solve for the quadratic function.
When playing with something like this, where the goal is normal and not perverse and not far away, the a-value of the trajectory curve, the coefficient of the quadratic term, is about as close as you can get at -2/3. Subsequently follow the trajectory and start upsetting the bacon, and you're sure to succeed within ten times.
Figure 15-Success!