# User:Cjcampo/ENES 100/Escher

## Problem

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.

## Conceive

Escher drawings can be drawn in 3D software and then physically modeled so their percularities become more exposed. Project doesn't have to include a water pump.

• This project has to have a chin rest system so the eye lines create the illusion.
• Videoing the illusion is a must
• Lighting is going to be very important

## Design

Ball up hill

Build work:

Build Instructions:

• cut out a 25cm by 12cm piece of cardboard to use the base
• cut out eight 2cm by 5cm pieces for the columns
• glue these pieces together long-wise to form two rectangular prisms
• cut out two 4cm by 4cm pieces and glue them centered to the tops of the columns
• glue the columns to the base so that the tops' edge is 19cm from the other
• cut out the ramp piece as shown in the picture
• The ends need to be 19cm apart, with the apex 5cm from the right end
• slightly bend the ramp in the apex
• glue ramp piece in between columns
• cut out two 2cm by 6cm rectangles
• cut slants into the two shorter ends as shown below
• cut out two more 2cm by 6cm pieces
• glue these long-ways to the pieces you just cut out as shown in the picture
• glue these supports to the base and the bottom of the ramp as pictured below
• coat everything with white paper
• fold 1cm wide strips of paper and glue them around the ramps and column tops
• this is so the balls don't roll off the ramps
• get a medium sized box
• cut out a hole so that a viewer can observe the illusion
• the hole's position can differ depending on the exact proportions of the model
• trace an outline of the model's base
• cut this square out about 2cm from the line, then cut the line out
• glue this frame into position in the box
Waterfall

Build work:

Waterpump work: Goal is to build method pumping Water up 1 foot. Here are some photos of making the siphon of different types.

### Objective

Creating a visional illusion against people's common sense of gravity.

### Background Design

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.

Technical drawings for the assembling the background

### Friction

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.

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.

Sliding Friction Data Tables and Videos

Different Surfaces at a 20 Degree Angle

Different Surfaces at a 30 Degree Angle

 Time for Objects to Go Down the Track at a 20 Degree Angle Surface Domino Jenga Block Piece of Wood Piece of Styrofoam Nothing on the track Time In Sec 1.0 4.2 0.0 0.0 1.2 1.3 0.0 0.0 1.1 4.0 0.0 0.0 Average 1.1 3.2 0.0 0.0 Painters Tape Time In Sec 0.7 0.9 1.2 0.0 0.8 0.9 1.0 0.0 0.8 0.8 1.2 0.0 Average 0.8 0.9 1.1 0.0 Sandpaper 100 Grit (Medium) Time In Sec 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Average 0.0 0.0 0.0 0.0 Sandpaper 220 Grit (Very Fine) Time In Sec 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Average 0.0 0.0 0.0 0.0
 Time for Objects to Go Down the Track at a 30 Degree Angle Surface Domino Jenga Block Piece of Wood Piece of Styrofoam Nothing on Track Time In Sec 1.3 1.5 4.4 0.0 1.0 2.2 2.7 0.0 1.1 2.7 2.6 0.0 Average 1.1 2.1 3.2 0.0 Painters Tape Time In Sec 1.0 0.9 0.9 5.4 0.8 0.8 0.8 3.9 0.9 1.0 1.0 3.9 Average 0.9 0.9 0.9 4.4 Sandpaper 100 Grit (Medium) Time In Sec 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Average 0.0 0.0 0.0 0.0 Sandpaper 220 Grit (Very Fine) Time In Sec 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Average 0.0 0.0 0.0 0.0 Aluminum Foil Time In Sec 1.3 1.1 1.0 0.0. 1.0 1.3 1.6 0.0 0.9 1.3 1.5 0.0 Average 1.1 1.2 1.4 0.0
Rolling Friction Data Tables and Videos

Different Surfaces at a 5 Degree Angle

Different Surfaces at a 10 Degree Angle

 Time for Marbles to Go Down the Track at a 3 Degree Angle Surface Big Marble Big Marble Small Marble Nothing on the track Time In Sec 1.44 1.51 1.05 1.73 1.35 1.39 1.53 1.60 0.98 1.38 1.63 1.14 1.69 1.36 1.35 Average 1.55 1.49 1.18 Painters Tape Time In Sec 1.96 1.45 1.37 1.45 1.42 1.80 1.29 1.65 1.62 1.43 1.70 1.65 1.31 1.72 1.59 Average 1.49 1.59 1.61 Sandpaper 100 Grit (Medium) Time In Sec 1.11 1.47 3.03 1.52 1.70 2.55 1.37 1.43 2.61 1.11 1.38 2.75 1.35 1.37 2.64 Average 1.29 1.47 2.72 Sandpaper 220 Grit (Very Fine) Time In Sec 1.38 1.32 1.70 1.35 1.43 1.94 1.33 1.56 2.09 1.58 1.55 1.87 1.67 1.41 1.89 Average 1.46 1.45 1.90
 Time for Objects to Go Down the Track at 5 and 10 Degree Angles Surface Big Marble Small Marble Glass Marble Plain Track at a 5 degree angle Time In Sec 1.72 1.69 1.59 1.67 1.72 1.64 1.73 1.64 1.63 Average 1.71 1.68 1.62 Plain Track at a 10 degree angle Time In Sec 1.06 1.30 1.34 1.08 1.41 1.24 1.12 1.41 1.34 Average 1.09 1.37 1.31 Foil at a 5 degree angle Time In Sec 1.83 2.03 1.72 1.82 2.02 1.66 1.87 2.04 1.98 Average 1.84 2.03 1.79 Foil at a 10 degree angle Time In Sec 1.76 1.57 1.60 1,25 1.40 1.48 1.41 1.51 1.42 Average 1.59 1.49 1.50 100 Sand Paper at a 5 Degree Angle Time In Sec 1.99 4.02 2.80 2.04 4.05 2.57 1.83 3.87 2.69 Average 1.95 3.98 2.69 100 Sand Paper at a 10 Degree Angle Time In Sec 1.36 1.69 1.45 1.31 1.64 1.39 1.34 1.71 1.66 Average 1.34 1.68 1.50 220 Sand Paper at a 5 Degree Angle Time In Sec 1.61 1.85 1.71 1.71 2.09 1.54 1.57 1.70 1.69 Average 1.63 1.88 1.65 220 Sand Paper at a 10 Degree Angle Time In Sec 1.29 1.17 1.19 1.01 1.43 1.19 1.26 1.33 1.16 Average 1.19 1.31 1.18
Bumper Track Data Tables and Videos

Different Surfaces on the Bumper Track

 Time for Objects to Go Down the Track Surface Big Marble Small Marble Glass Marble Plain Bumper Track Time In Sec 1.79 1.31 1.36 1.69 1.75 2.02 1.74 1.64 1.89 Average 1.74 1.57 1.76 Aluminum Foil on the Bottom Time In Sec 1.71 1.61 1.76 1.44 1.73 1.80 1.60 1.73 1.60 Average 1.58 1.69 1.72 Sandpaper 100 Grit (Medium) on the Bottom Time In Sec 1.34 2.03 1.35 1.39 1.49 1.65 1.73 1.53 1.59 Average 1.49 1.68 1.53 Sandpaper 220 Grit (Very Fine) on the Bottom Time In Sec 1.33 1.82 1.58 1.60 1.79 1.75 1.44 1.89 1.68 Average 1.46 1.83 1.67
Friction Formulas and Calculations

Rolling Friction

Formula is F= (I×α)÷R

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

Design:
Below is the initial computer aided drawing, this drawing is from the angle that will make the illusion possible.

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:

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.

```                                                              Trial 1: 3.63 seconds
Trial 2: 3.67 seconds
Trial 3: 3.59 seconds
Trial 4: 3.63 seconds
Trial 5: 3.65 seconds
Trial 6: 3.71 seconds
```

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.

## Implement

Escher Demo Projectː Marble rolling against gravity

Prototypes

## Operate

Escher Demo Projectː Marble rolling against gravity

## Demo

Escher Demo Projectː Marble rolling against gravity

## Next Steps

Ball/Water Flowing Uphill
• Paint the track a dark color so it reduces shadows
• Create a white background to show the illusion
• Create a steady camera stand to film so it is not shaky
• Complete the third tier to the design
• Test the Track and refine the design and make a larger scale design
• Determine whether to use a ball or water
• Try different liquids to see if the illusion works better with slower flowing liquids or faster flowing liquids
Ball up hill
• Make video of 2 ramp
• Create demo of the 2 ramp
• Draw water fall
• Make the four ramp
• Create successful physics simulation using track variations