A nice explanation, from the excellent Real Engineering channel, of the physics of GPS that explains how the satellites must adjust for the effects of special and general relativity.
Generating 3d Terrain
After a lot of hours of experimentation I’ve finally settled on a workable method for generating large-scale 3d terrain.
Data from the NGDC’s Grid Extraction tool. The ETOPO1 (bedrock) option gives topography and bathymetry. You can select a rectangle from a map, but it can’t be too big and, which is quite annoying, you can’t cross the antimeridian.
The ETOPO1 data is downloaded as a GeoTIFF, which can be easily converted to a png (I use ImageMagick convert).
Adjusting the color scale. One interesting property of the data is that it uses a grayscale to represent the elevations that tops out at white at sea-level, then switches to black and starts from there for land (see the above image). While this makes it easy to see the land in the image, it needs to be adjusted to get a good heightmap for the 3d model. So I wrote a python script that uses matplotlib to read in the png image as an array and then I modify the values. I use it to output two images: one of the topography and one of just land and water that I’ll use as a mask later on.
The images I export using matplotlib as grayscale png’s, which can be opened in OpenSCAD using the surface command, and then saved as an stl file. Bigger image files are take longer. A 1000×1000 image will take a few minutes on my computer to save, however the stl file can be imported into 3d software to do with as you will.
Note: H.G. Deitz has a good summary of free tools for Converting Images Into OpenSCAD Models
Bike Silhouette
One of my students with a TechShop membership wanted a bike silhouette for a wall hanging. He wanted it to be bigger than he could fit on the laser cutter, so I tried doing it on the CNC router. The problem was that to get the maximum detail we needed to use the smaller drill bits (0.125 inches in diameter), however, after breaking three bits (cheap ones from Harbor Freight) and trying both plywood and MDF, we gave up and just used the larger (0.25 inch) bit. Since the silhouette was fairly large (about 45 inches long), it worked out quite well.
How to Build an 8-bit Computer on a Breadboard
Ben Eater’s excellent series on building a computer from some basic components. It goes how things work from the transistors to latches and flip-flops to the architecture of the main circuits (clock, registers etc). The full playlist.
Other good resources include:
- Nand2Tetris : Building a computer from first principles (this one uses a hardware simulator however): See overview video.
Cell Phone Shelf
Managing cell phone usage at school is a tricky topic. We have some teachers who’d like to ban them outright, but we also have a growing number of parents who are expecting to be able to communicate with their kids–to organize pickups and carpooling during the day for example. The phones can be great for data-collection and documentation in classes, and a lot of my upper level math students prefer the Desmos app to using their graphical calculators.
Our current compromise is that middle schoolers have to leave their phones in the front office, where they can check them at lunch time or check them out if a teacher wants them to use them.
The high schoolers are allowed to keep their phones with them, but have to put them in a basket at the front of the classroom. Since they don’t like piling them into the basket, I experimented with the CNC machine to cut some plywood into a cell-phone shelf.
The shelf can hold about 30 phones, and I can easily see how many phones are on there from across the room, so I’d say this one worked out pretty well.
Go Board
I recently discovered that, although they may look it, Go boards are not necessarily square. They’re slightly longer in one dimension so that the board looks more square to the players on both sides.
A student asked me to make one for him–he’d ordered a set recently and didn’t like the board it came with–so, I wrote a small python program to generate the Go grid, then lasered it onto a nice piece of sanded plywood.
It worked out quite well. Apparently the plywood makes just the right “thunk” sound when you put down the pieces.
The script to generate the grid.
go_board_2.py
from visual import *
from svgInator_3 import *
length = 424.2 #mm
width = 454.5 #mm
nLines = 19
dx = length/(nLines-1)
dy = width/(nLines-1)
print "Lenght = ", length
print "dx = ", dx
f = svgInator("go_board.svg")
lineStyle = {"stroke": "#000", "stroke-width": "2pt",}
#lines
for i in range(nLines):
x = i * dx
y = i * dy
#vertical
f.line(pos=[vector(x,0), vector(x,width)], style=lineStyle)
#horizontal
f.line(pos=[vector(0,y), vector(length,y)], style=lineStyle)
#circles
grid_pos = [(3,3), (3,9), (3,15),
(9,3), (9,9), (9,15),
(15,3), (15,9), (15,15)]
for i in grid_pos:
(x, y) = (i[0]*dx, i[1]*dy)
f.circle(pos=vector(x,y), radius=2.0,
style={"stroke": "#000", "fill":"#000"})
#bounding box
f.rect(dim=vector(length,width), style=lineStyle)
f.close()
Now I just have to learn to play.
Our Natural Bridge
Inspired by a video of a temporary bridge built out in the woods for mountain biking, my students wanted to try building a “natural” bridge with no fasteners–no screws, no nails–over a small ravine that feeds into our creek.
We found a couple large fallen logs to cut into two 10 foot lengths for the basic structural support for the bridge. These were dug into the ground to anchor them on either side of the ravine. We then chopped a couple more logs into 2 foot sections to go across the structural logs. The dense mud from the banks of the creek was then packed onto the top to hold it all together.
In the end, the bridge turned out to be pretty solid, and definitely usable.
Building Bridges (Literally)
My crew from the Gaga Ball pit decided to make a trail through the woods and across the creek. So they built two short (12 ft long) bridges to cross the creek itself, and a third, “natural” log bridge to cross a small ravine that runs into the creek and cuts across the trail.
The short bridges were made of overlapping 2×4’s for structure (held together by 2.75 inch structural screws), with 24 inch long, 1×6 planks across the top.
The short bridges needed to be small and light enough to be moved when the creek rises, like it did today. I’ll attest that they can be moved, but not easily. They’re pretty heavy: it took a team of three or four middle schoolers to get it down to the creek, and it was hard going trying to drag it over to the side by myself this afternoon. Note to self: next time make sure the structural cross pieces are not at the very end of the bridge.
