New Shepard is NOT in Orbit

Posted by Justin A. Parr on July 20, 2021
Posted in: Math and Science. Leave a Comment

This morning, July 20, 2021, Blue Origin’s New Shepard rocket launched in to space for its first 11-minute passenger flight.

Congrats to Bezos and team!

HOWEVER, the commentator on one of the science channels made this statement:  “The rocket needs to go high enough to reach orbit, even briefly”

A popular misconception is that orbit and outer space are the same thing – actually, I’ve written about this previously.  However, I would expect a science commentator on a science-related channel to know the difference!

Just to recap:

  • The Kármán Line, at 100Km (about 62 miles) above the Earth’s surface is considered for treaty purposes to be the delineator between the Earth and “outer space”.  From what I can tell, New Shepard will briefly surpass this, making all of its passengers “official” astronauts.
  • For reference, the International Space Station’s orbit fluctuates, but the average is about 240 miles above Earth’s surface.
  • Reaching outer space doesn’t automatically mean that you are in orbit, nor that you somehow magically become weightless.

Even hundreds of thousands of miles away from the surface, any object is still within the Earth’s gravitational influence.  So, if you fire a rocket straight up (perpendicular to the Earth’s surface), even hundreds or even thousands of miles in to space, eventually, the rocket will run out of fuel, and the Earth’s gravity will pull it back down.

In orbit, however, an object’s velocity parallel to the Earth’s surface creates centrifugal force which balances the pull gravity.

E. A rocket launched perpendicular to the Earth’s surface eventually runs out of fuel and is pulled back down by gravity. F. To achieve orbit, a rocket must attain both height and velocity parallel to the surface.

My understanding of New Shepard is that it will basically travel straight up, give the passengers a few minutes of weightlessness, and then return to Earth.

Although gravity will be acting on the spaceship and its passengers during the descent, the passengers will experience weightlessness (which is different than outer space and also different than orbit) because gravity acts on both nearly-equally.  The state or sensation of weightlessness occurs when there are no net forces acting on the passengers, which is only true inside the ship, and only relative to the ship itself.

Although the exact height of the New Shepard’s mission isn’t listed, it is expected to go “well above” the Kármán Line.  So if we were to guess 65 miles, we would be in the right ball park.

This means that New Shepard’s velocity at 65 miles above the Earth’s surface will be zero, after its rockets turn off, and gravity bleeds away all of its upward velocity.  At that exact point, with gravity acting constantly, it will begin to accelerate back down to Earth.  Until the ship hits turbulence in the atmosphere, or they fire their re-entry rocket, the passengers will continue to fall at an ever faster rate toward Earth, pulled by gravity, yet experiencing weightlessness within the ship.

In contrast, to attain orbit at 65 miles above the Earth’s surface, the ship would have to be travelling almost 17,780 miles per hour parallel to the Earth’s surface in order to have enough centrifugal force to exactly counter the force of gravity.

How do we go about calculating this?  Glad you asked…

Force of gravity:

F = m ⋅ g

  • m = mass of the object
  • g = acceleration due to gravity

Centrifugal force (same as centripetal force, but in the opposite direction):

F = m ⋅ v2
r

  • m = mass of the object
  • v = linear velocity
  • r = radius of the orbit (from the center of the Earth)

In orbit, the net force is zero, so:

m ⋅ g = m ⋅ v2
r

We quickly see that mass is irrelevant, and we can solve for v:

v = √ g ⋅ r 

If we measure gravity and orbital radius in feet, we get orbital velocity in feet per second.  To simplify things, we can use 78,545 miles per hour2 as the acceleration due to gravity:

v = √ 78545 ⋅ r 

The radius of the Earth is about 3960 miles.  To find orbital velocity, we have to have the radius from the center of the Earth, which include’s the Earth’s radius plus the height above the surface:

v = √ 78545 ⋅ ( 3960 + r ) 

If we plug in 65 miles, we get about 17,780 miles per hour required for orbit.

So again, good luck to Bezos and team – although you won’t be “in orbit”, you will definitely be in outer space.

Guns – Handgun State Diagram (Automatic), and Common Movie Continuity Errors

Posted by Justin A. Parr on May 7, 2021
Posted in: Good Design - Bad Design, The Light Side. Leave a Comment

Previously, I’ve written about gun-related movie myths in “Movie Myths: Guns – Part 1“, and in there, I described in detail how guns work – both automatics and revolvers.

Since that time, I’ve thought about making a state diagram that helps explain some of the common gun-related continuity errors that you regularly see in movies and TV.

The result is the diagram that you will see in this article, along with a higher-resolution PNG and PDF that you can download for free, which would make a nice wall decoration for any gun enthusiast.

Download the PDF here, or the PNG here.

Read on for more information about state diagrams and gun-related movie continuity errors…

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Find the Center of a Circle Using Only a Pencil and Straight Edge

Posted by Justin A. Parr on February 18, 2021
Posted in: Math and Science, Tech Tip. 1 comment

Find the Center of a Circle Using Only a Pencil and Straight Edge

I bought a wood lathe recently, and the first time I tried to center some wood, I went through the painful process of remembering how to find the center of a circle.  This, despite having had three years of mechanical drawing classes.

Starting with a pencil and straight edge:

  1. Mark a line on the straight edge that’s a little more than 3/4 of the diameter (height) of the circle.  It doesn’t have to be exact.
  2. Make a mark (M) at the top of the circle.  The location of the mark need not be exact.
  3. Align the straight edge so that the corner is on mark M, and the line on the straight edge touches the right edge of the circle.  Draw a line (A) from somewhere above the center of the circle out to it’s edge.
  4. Repeat on the left side, drawing line B.
  5. From where line B ends, line up the straight edge so that its corner sits on the end of line B, and its line touches the lower-right-hand edge of the circle.  Draw line C along the straight edge, crossing the vertical center line.
  6. Repeat from the end of line A to the lower-left-hand edge of the circle, and draw line D
  7. At this point, lines C and D should form an “X” near the bottom of the circle.
  8. Draw a vertical center line (E) by aligning the straight edge with mark M and the intersection of lines C and D.  Start the line above the center, and go all the way to the bottom edge.
  9. At this point, line E passes through the center vertically, but we need to find the horizontal center.
  10. From where line E touches the bottom of the circle, align the straight edge so that it crosses line A, and the line on the straight edge touches the upper-right-hand edge of the circle.  Draw line F, crossing line A.
  11. Repeat this on the left side, crossing line B, and drawing line G.
  12. At this point, there should be an “X” on the left formed by lines B and G, and one on the right formed by lines A and F.
  13. Align the straight edge across the intersections of the left (B,G) and right (A,F) intersections, and draw the horizontal center line H.

The center of the circle is at the intersection of the vertical (E) and horizontal (H) center lines.

 

How This Works

Let’s call the distance from the corner of the straight edge to its mark S.

Let’s call the points where the horizontal center line meets the circle’s edges H1 (left) and H2  (right), and the point where the vertical center line meets the bottom V.

If we start at M and walk clockwise around the circle, we would pass through the points as follows:  M (start) → H2 → V → H1 → M (back to start).

If the radius is 1, then the diameter is 2, and the length of MH2 is 1.41. We initially selected S to be about 3/4 of the diameter, or about 1.5.

The circle’s radius, R, is 1/2 the length of MV or H1H2.  The length of MH2 would be √ R2 + R2 , and the same is true for H2V, VH1, and H1M.

If we assume that the radius R is “1 unit” (the actual length is irrelevant), then √ 12 + 12 = √ 2 , or about 1.41.

If the radius R = “1 unit” then the diameter = 2 ⋅ R = “2 units”.

By selecting S such that S is 3/4 of the diameter, 3/4 ⋅ 2 = 1.5.  Since S>1.41, and we make two consecutive S-length marks around the circle, we know for a fact that 2 ⋅ S is greater than the length of MH2V.

By doing this twice, once clockwise, and once counterclockwise, we get lines C and D.  We can call their intersection point T

MAD = MBC = 2⋅S. Point T is located at the intersection of lines C and D. Triangles ΔMAT and ΔMBT are congruent. MT bisects AB.

⋅

It’s easy to prove that this forms two congruent triangles:  ΔMAT and ΔMBT.  If the line MT is the base of both, then because they are congruent, the height of both are the same, which means that MT perfectly bisects AB).

Since this line MT also bisects the equilateral triangle ΔMAB which is inscribed within the circle, that line must pass through the center of the circle as well.

Carrying MT out to the edge of the circle gives us point V.

By drawing a line from V of length S to the edge, we get line F, which crosses line A.  We can call this intersection point U.

Points U and W are at the intersections of A and F, and B and G respectively. MUV is equilateral because MU=UV. MUV is congruent to MWV.

If we knew where the center of the circle (point O) was located, we could make the congruent triangle argument, that ΔMUO is congruent to ΔVUO, and just as with the vertical center line bisecting ΔMAB, UO would perfectly bisect the larger equilateral triangle ΔMUV.

On the other side, we draw line G of length S, which crosses line B at point W.  Same congruency argument:  ΔMWO is congruent to ΔVWO, and WO bisects equilateral triangle ΔMWV.

Because MU = VU we know that ΔMUV is equilateral, and the same for ΔMWV.  Further, because of the congruency argument, we know that MU = MW and VU = VW, and therefore ΔMUV is congruent to ΔMWV.

If line UO bisects triangle ΔMUV, then it must intersect MV exactly at its center.  Same for WO and triangle ΔMWV.

Therefore, WU passes through the center of both triangles at point O, where WU intersects MV.

And therefore, point O must be at the center of the circle, because VO = MO, and we know that MV passes through the center of the circle.

Note that this trick ONLY works if the the mark on the ruler (distance S) is > 1.41 times the radius.

Justin’s Perfect Quiche – Build-Your-Own

Posted by Justin A. Parr on November 30, 2020
Posted in: Food and Cooking. 1 comment

Justin’s Perfect Quiche – Build-Your-Own

I make quiche once or twice per year, and I don’t have a specific recipe that I follow – I usually google for things like portions, temperature, and cooking time.

This year, I decided to take some notes and provide a general quiche framework that will work for any kind of quiche you want.

The goal is to have 4 cups of eggs, cheese, plus other stuff (filler ingredients) that we pour in to a 9″ pie crust.  Although a 9″ pie crust will hold about 5 cups, the quiche will rise during the cooking process.

One major tweak from “normal” quiche recipes:  Instead of milk, I use sour cream, which has much more fat in it and also significantly improves the flavor.  Because sour cream is more dense, I use bread (chopped up) so that you don’t end up with a 2″ thick egg-crete block.

Equipment:

  • 9″ Pie Pan, greased, and a sheet pan to bake it on
  • Mixing Bowl (I usually skip the mixing bowl, and just mix the ingredients in the 4-cup measure)
  • Whisk
  • Cutting board and knife as needed for bread and other “filler” ingredients
  • 4 Cup measure
  • Sautee pan and wooden spatula – if you use cooked ingredients, the pan and spatula are not needed

Ingredients:

  • 9″ Pie Crust
  • 2 to 3 slices of bread
  • 8 to 12 eggs
  • 1/2 to 3/4 cup of sour cream
  • 2 Tbsp of brown mustard
  • 1 cup of shredded cheese
  • 1 to 2 cups of filler ingredients
  • 2 Tbsp of oil or butter to sautee ingredients – if you use cooked ingredients, the oil or butter is not needed
  • Salt, pepper, garlic powder, onion powder to taste.  About 1/2 teaspoon each.

Note:

  • For every 4 eggs, use 1 slice of bread and about 1/4 cup of sour cream.
  • If you have more filler ingredients, use fewer eggs – minimum of about 8.  If you have fewer filler ingredients, you’ll need more eggs, and thus more bread and more sour cream.
  • Makes at least 8 portions
  • About 20 minutes prep time, and about 1 hour 30 minutes cook time, which includes 15 minutes of resting time, or about 1 hour 50 minutes total.

Preparation:

  1. For any raw filler ingredients, cut them in to small slices or bite-sized pieces, and sautee them in the sautee pan until tender.  They don’t need to be cooked to annihilation, just cooked to the point of tender.  Let them cool.
  2. For any ingredients that are already cooked, such as ham, bacon, or other leftover meat, cut them in to small bite-sized pieces.
  3. Preheat oven to 375.
  4. Grease the pie pan and lay out the pie crust, crimping or folding the edges as you would with any other kind of pie.

Cooking:

  1. Cut the crusts off the bread, and cut the bread in to small cubes.
  2. Add the following in to the mixing bowl, then whisk until the eggs are fluffy:
    • Eggs – at least 8
    • Sour cream – at least 1/2 cup
    • Brown mustard
    • Salt, pepper, and optionally, garlic powder and onion powder.
  3. Add the following in to the mixing bowl, then stir
    • Bread (cubed, with crusts removed)
    • Shredded Cheese (about 1 cup)
    • Filler ingredients (Pre-cooked and cut in to bite-sized pieces)
  4. Pour all of this in to a 4 cup measure.  At this point, in the mixing bowl, mix up some additional eggs if needed.  If you have 3 cups of stuff, you need to add about 4 eggs.  If you have 3-1/2 cups, you need to add about 2 eggs, etc…
  5. At the point where you have 4 full cups of eggs + other stuff mixed and sitting in the 4-cup measure, carefully pour all of it in to the center of the pie crust.
  6. Place the (now-filled) pie pan on top of the sheet pan (in case it spills over), and place both in the pre-heated oven.
  7. Bake for 375 for up to 75 minutes.  Check the center at about 50 or 60 minutes, and monitor closely until the entire thing is solid.  It will rise about 1/2″ to 1″ during the baking process.
  8. Remove from the oven and let stand for about 15 minutes.
  9. Cut in to slices and serve.

Troubleshooting FTP

Posted by Justin A. Parr on November 29, 2020
Posted in: Rants, Tech Support. Leave a Comment

[Edits, 7/28/2022:  There were a couple of technical clarifications required]

Let me start off by saying “I HATE FTP!”

It was developed in the early 1970’s, before the Internet was really the Internet, and before the existence of firewalls or any other type of network security.  Over the last nearly-50 years, it has picked up so many band-aids that the entire protocol is now just basically one big kludge.

Despite its shortcomings, and despite the availability of newer and far superior file transfer tools, banks, governments, and anyone else with a mainframe continues to use it.

So, unfortunately, people like you and I get stuck supporting it.

If you’re having an FTP problem, or are just morbidly curious to learn about an antiquated protocol, read on…

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