Sunday, February 9, 2020

Physics in the playground II: The tree

There's a tree standing in the Walnut Hills Park playground ( one of the playgrounds, that is). I think it's some kind of fruit tree but there are no leaves on it and I'm not a tree identification expert. Here's the tree.

The real reason I did this was the new app I downloaded. Dioptra is a software version of my surveyor's compass. It gives me all the angles utilizing the accelerometers and the magnetometers in my phone.

We looked at the accelerometers last time.

Phones that have  built-in magnetometers use them for an onboard compass. Apps like Science Journal can use them to directly measure magnetic and electric fields.

Magnetometers in phones usually sense changes in conductivity in tiny electronic devices when they are exposed to a magnetic field. 

The phone has three magnetometers in one and they're aligned, just like the accelerometers along the x, y, and z planes, so the phone can sense the direction of a magnetic field.

Here's what the Dioptra screen looks like.

I aim with the crosshairs and the scales tell me directions. The curved scale on the left is a level. It tells me how much the phone is tilting. The data above it gives me my position in space and time: date and time, latitude and longitude, altitude, and error (CEP stands for circular error probable. For those in statistics, it's a 50% confidence interval for measurements within a circle.) I can set the app for different units.

The scale at the bottom is the compass reading for line-of-sight and the numbers above it makes it explicit. Those are the azimuth and bearings. Azimuth is the degrees of the angle between line-of-sight and due north. The bearing is the same in compass directions.

The scale to the right is the incline of the sight-line to horizontal. So, here's my sight-line to the tree top.

The phone is 4 degrees off level...ah, who cares. The location data is not important to what I'm doing, so I'll ignore it.  The GPS data could be as much as 30 feet off. That won't affect the accelerometers. My line-of-sight, just in case you're interested, is nearly southwest, 232 degrees from North and 52 degrees southwest,
but that won't play in our calculations either.

What I need is the inclination, which is 43.6 degrees from horizontal. You might have noticed that I have a tape measure in the first photo above. I was 20 feet from the base of the tree when I shot this line. That means that I have a right triangle with a base (adjacent side to my position) of 20 feet and the angle where I stood was 43.6 degrees. What I want is the length of the opposite side (height of tree). I can get that in several ways but I think I'll go with tan(angle)=opposite side/adjacent side. That shuffles around to opposite side=tan(angle) times adjacent side, or the length I want is the tangent of 43.6 degrees times 20 feet.

The height of the tree above my eye level is 19.05 feet. My eye level is 5.5 feet off the ground so that makes the tree 24.5 feet high.

I did the calculations on my MC50 calculator app.

The Dioptra app is put out by Workshop512 and the MC50 calculator by Walter Stubbs.

It's pretty impressive what phone apps will do. If you need your phone to do something that it doesn't already do, check your app store. Check out the rating, reviews, and app description before downloading. Advertisements are not usually a big problem but some of these apps are clogged up with ads. Some of the apps have a price and some are free but have a better version that you can buy. The prices are usually very reasonable.

Next time, I send a phone down a spiral ramp on a crash course.

Although the Dioptra app does everything my surveyor's compass does, I'm not ready to get rid of the compass. In the first place, it's very small. Also, it will never need a battery change or charge.

No comments: