Escher drawings can be made into 3D objects that if looked at in the right lighting, at the right angle, create an illusion ... typically of water going up hill or balls rolling up hill. These illusions make great demonstration devices that illustrate engineering and art to kids and start interesting conversations.
Background design incorporated in the initial prototype
Overview of the first Prototype
Second Background design
Instead of tilting one side of the bottom, for the second background design, two sides of the bottom were tilted 15 degrees, which means there is a corner touching the ground.
Escher background front view
Escher background1 back view
Escher background side view
Escher background top view
Escher background (bird-eye)
Technical drawings for the assembling the background
Project prototype with sandpaper on top. It has a 3 degree angle.
Plain track
Painter's tape on the track
Aluminum foil on the track
100 grit sandpaper on the track
220 grit sandpaper on the track
Aluminum foil at a 5 degree angle
100 grit sandpaper at a 10 degree angle
Painter's tape at a 20 degree angle
100 grit sandpaper on a 30 degree angle
Test objects
The way friction was tested in this project was by taking a big marble, a little marble, a glass marble, a domino, a piece of wood, a Jenga block and a piece of styrofoam and running them down tracks covered in painter's tape, 100 and 220 grit sandpaper and aluminum foil. Then comparing the time to the plain track. This was done at 3, 5, 10, 20 and 30 degree angles. The average time was taken in seconds over three separate trails.
Results
At 3 Degree Angle
The material that had the fastest time was the small marble on the plain track. The material that had the slowest time was the small marble on 100 grit sandpaper.
At 5 Degree Angle
The material that had the fastest time was the glass marble on the plain track. The material that had the slowest time was the small marble on 100 grit sandpaper.
At 10 Degree Angle
The material that had the fastest time was the big marble on the plain track. The material that had the slowest time was the small marble on 100 grit sandpaper.
At 20 Degree Angle
The material that had the fastest time was a domino on the painter's tape. The material that had the slowest time was a Jenga block on the plain track.
At 30 Degree Angle
The materials that had the fastest time were a domino, a piece of wood and a Jenga block on the painter's tape. The material that had the slowest time was a piece of styrofoam on the painter's tape.
Bumper Track Plain
Bumper Track With Aluminum Foil
Bumpr Track With 100 Grit Sandpaper
Bumper Track With 220 Grit Sandpaper
The way friction was tested in this part of the project was by taking a big marble, a little marble and a glass marble and running them down the bumper track covered in 100 and 220 grit sandpaper and aluminum foil. Then comparing the time to the plain track. The average time was taken in seconds over three separate trails.
The 220 grit sandpaper was the material that made the most difference for all three marbles. It had the fastest time with the small marble and the slowest time with the big marble.
The I= (2÷5) MR² and stands for rotational inertia.
The α= (5×g×sin θ)÷ 7R and stands for angular acceleration.
The final formula for F= (2×g×sin θ) ÷ 7
g= 9.8
Calculation of Friction for the Angles of 3, 5, and 10 Degrees
Weigh
Object
Big Marble
8.368 g
Small Marble
1.044 g
Glass Marble
1.437 g
G = 9.8 m/s
Sin ϴ = 3, 5 or 10 (depending on which angle is being used)
Object
Sin ϴ = 3
Sin ϴ = 5
Sin ϴ = 10
Big Marble
(2×8.368 ×9.8 × sin 3) ÷ 7 = 3.306 gsec²
(2×8.368 ×9.8 × sin 5) ÷ 7 = -22.4679 gsec²
(2×8.368 ×9.8 × sin 10) ÷ 7 = -12.7466 gsec²
Small Marble
(2×1.044 ×9.8 × sin 3) ÷ 7 = 0.4125 gsec²
(2×1.044 ×9.8 × sin 5) ÷ 7 = -2.803 gsec²
(2×1.044 ×9.8 × sin 10) ÷ 7 = -1.5902 gsec²
Glass Marble
(2×1.437 ×9.8 × sin 3) ÷ 7 = 0.5678 gsec²
(2×1.437 ×9.8 × sin 5) ÷ 7 = -3.8583 gsec²
(2×1.437 ×9.8 × sin 10) ÷ 7 = - 2.1889 gsec²
Sliding Friction Formula
Ff = (μ)(N)
N= (g)(m)(cos ϴ)
Ff = (μ)( g)(m)(cos ϴ)
where
Ff = frictional force
μ = static (μs) or kinetic (μk) frictional coefficient
N = normal force
Ff - Frictional Force
μ - coefficient of friction on different surfaces
g - acceleration due to gravity which is constant at 9.8
m - mass of the object
cos ϴ - angle of the board or whatever surface the object is sliding down
Calculation of Friction for the Angles of 20 and 30 Degrees
Weigh
Object
Domino (plastic)
18.442 g
Jenga Block (wood)
14.561 g
Piece of Wood
10 g
Surface
μ
Plasatic on Plastic
0.5
Wood on Plastic
0.174
Wood on Sand Paper 100 Grit
1.23
Wood on Sand Paper 220 Grit
0.749
Wood on Aluminum
0.04
G = 9.8 m/s
Cos ϴ = 20 or 30 (depending on which angle is being used)
Object
Surface
Cos ϴ = 20
Cos ϴ = 30
Domino
Plasatic on Plastic
18.442 * 9.8* 0.5 * Cos 20 = 84.916 gm/s
18.442 * 9.8* 0.5 * Cos 30 = 78.259 gm/s
Jenga Block
Wood on Plastic
14.561 * 9.8 * 0.174 * Cos 20 = 23.332 gm/s
14.561 * 9.8 * 0.174 * Cos 30 = 21.502 gm/s
Wood on Sand Paper 100 Grit
14.561 * 9.8 * 1.23 * Cos 20 = 164.933 gm/s
14.561 * 9.8 * 1.23 * Cos 30 = 152.003 gm/s
Wood on Sand Paper 220 Grit
14.561 * 9.8 * 0.749 * Cos 20 = 100.435 gm/s
14.561 * 9.8 * 0.749 * Cos 30 = 92.561 gm/s
Wood on Aluminum
14.561 * 9.8 * 0.04 * Cos 20 = 5.364 gm/s
14.561 * 9.8 * 0.04 * Cos 30 = 4.943 gm/s
Piece of Wood
Wood on Plastic
10 * 9.8 * 0.174 * Cos 20 = 16.023 gm/s
10 * 9.8 * 0.174 * Cos 30 = 14.767 gm/s
Wood on Sand Paper 100 Grit
10 * 9.8 * 1.23 * Cos 20 = 113.270 gm/s
10 * 9.8 * 1.23 * Cos 30 = 104.390 gm/s
Wood on Sand Paper 220 Grit
10 * 9.8 * 0.749 * Cos 20 = 68.975 gm/s
10 * 9.8 * 0.749 * Cos 30 = 63.568 gm/s
Wood on Aluminum
10 * 9.8 * 0.04 * Cos 20 = 3.684 gm/s
10 * 9.8 * 0.04 * Cos 30 = 3.395 gm/s
Ball/Water flowing Uphill
Our design is based off of an MC Escher waterfall drawing. The bottom track will be flush with the ground. The second tier of the project is the part which looks like the illusion. The bottom track is about 2 inches wide and is roughly a total length of like 21 inches. The angles will be at about 45 degrees when the design is completely finished. Also the design will be extruded so it looks more like a track but the picture is a birds eye view of what it will look like and those are the dimensions of the bottom track.
This track is made of balsa wood which is very light which means it is very brittle in the sense that it could fall apart if water is added to it. Might have to find a substitute like a ball or marbles. If water is added it may show lots of leaks and a solution might be to have to add a caulk like material to seal off the edges of the track. Also this shows a Rough view of what the illusion will look like when the camera is on the track.
Project Goal:
Using the M.C. Escher artwork titled: Waterfall, design and build a 3D replica that will create the illusion of a marble rolling against gravity, up the track and falling down from above, which will contain aspects of perpetual motion.
M.C. Escher: Waterfall
Waterfall by M.C. Escher A surrealist work from the 1960's
Design:
Below is the initial computer aided drawing, this drawing is from the angle that will make the illusion possible.
initial drawing
Building: Materials:
Poster/Foam board
Box Cutter
Ruler
Duct Tape
Plastic Sticks
Step 1:
Measure and cut pieces of foam board 6 total:
2.5in by 10in
2.5in by 8in: Twice
2.5in by 6in: Twice
2.5in by 4in
Attach pieces using duct tape to create bottom track and 3rd level upper tier of the design.
Measure and cut 8 pieces of foam board, these will make up the side rails of the tracks:
1.25in by 10in: twice
1.25in by 8in: Four times
1.25in by 6in: Four times
1.25in by 4in: twice
Attach pieces on either side of the tracks as side rails to help keep the marble from rolling off.
This is the finished 1st prototype of the Escher Waterfall:
This angle is the one which holds the illusion
all three levels at the illusion angle
Implement:
Due to the fact that a marble is being used instead of water to create the gravity defying illusion, this project will be reliant on timing and the use of multiple marbles. It will consist of an initial marble that rolls from the beginning of the track to the end in the background, then when the marble reaches the end of the ground level track, a marble will be released on the top level track and roll forwards and fall down to the ground level track and start the cycle over again. As mentioned before, timing will be critical in this illusion, therefore initial bottom track tests trials were conducted to find an average time it takes for a marble to roll from the beginning to the end of the ground level track.
Next Steps
The next step to bring this illusion together is to design a mechanism that will launch balls from the top level of the structure and have them fall to the lower level and roll to the background. This is imperative to the illusion because it needs to seem like there is a perpetual cycle that the ball just continues to roll up and fall down non-stop and forever. However, this illusion will not work unless there is a way to eliminate the background, as well as the shadows which take away from the illusion. The proposed background will be a flat black and the track will end up being painted a flat black or dark grey color in order to eliminate shadows and anything else that will distract from the illusion.