Science & Nature Archive

Wednesday, February 13, 2019

Weighing Myself Over a Whole Day

Detecto Bathroom ScaleEver since I posted an entry about the techniques I found useful to lose weight (How I Lost 40 lbs in 6 Months), there's been a project that I've wanted to do, but I just got around to doing yesterday. I weighed myself continuously over a whole day to see how my weight varied.

In that older entry, I'd mentioned that one of the techniques I found useful was weighing myself daily. I explained how I did so in the mornings in only my underwear to try for consistency, and also how you shouldn't stress too much over small fluctuations. And while I knew from experience that my weight could vary by pounds over the course of the day, I'd never taken a detailed look to see exactly what that looked like. So I finally did. (It was actually a little bit more of a hassle than I'd anticipated, so don't expect another entry like this any time soon.)

Before getting into the longer explanation, here are the results, in two graphs. The first graph includes my body weight and the full weight on the scale (i.e. with clothes throughout most of the day). The second is just my body weight, so that the graph could be 'zoomed in' a bit more. Both graphs also include the next morning, just to help show the trend.

My heaviest body weight over the course of the first day was right after lunch, at 171.6 lbs. My lightest was right before supper, at 167.6 lbs. So, over the course of that day, my body weight varied by 4 lbs. Also, my clothes weighed around 5 ½ lbs, so my biggest number on the scale was 177.1, almost 10 lbs heavier than my lightest body weight.

Weight Over a Whole Day (Includes uncorrected scale weights)
Click to embiggen
Body Weight Over a Whole Day
Click to embiggen

Let's get into a few more details. First, here's my schedule over that period. I was up a bit late the night before, going to bed at midnight. I woke up at 6:00, made a quick trip to purge my bladder, then did my morning workout. Once I got to work, an office job, I ate my breakfast and started drinking coffee, making periodic bathroom breaks. Pretty much every sudden drop in weight throughout the day was a bathroom break, so I won't bring those up again. I ate my lunch at 11:00. For the rest of the afternoon, I tapered off on the coffee, with a protein bar snack around 12:30. I ate supper around 6:00, then changed to work clothes to go help my daughter on some projects at her house, having a drink or two of diet soda over there. I got home and went to bed around 10:00.

I didn't eat that much yesterday, not anywhere close to what I eat on weekends or special occasions. I'm pretty sure that if I did this on a Saturday, there would be much bigger spikes at meal times.

One thing I already knew, but which I still think is interesting, is how much my body weight drops while I'm sleeping - around a pound. I'm guessing this is a combination of basal metabolic rate (inhaling oxygen, but exhaling the slightly heavier carbon dioxide), perspiration, and losing just a bit of water to evaporation while breathing.

I had no intention to strip down to my underwear every time I was going to weigh myself, so I just did some math. I weighed myself with and without clothes in the morning before heading to work, and then again when I got home to get a pair of measurements for my office clothes. Then I did the same thing before and after heading to my daughter's house to get a pair of measurements for my work clothes. So, for each outfit, I had two measurements for the difference. I averaged it for each, and subtracted that from the weight on the scale. (It turned out to be right around 5.5 lbs for both outfits.) And to be thorough, I even made sure my pocket contents were the same each time I weighed myself (cell phone, wallet, keys, pocket knife, and mini tape measure at work, empty pockets at my daughter's).

That last paragraph brings up another caveat - my scale's not perfect. If it was, it should have shown the same difference in weight in clothes before and after work, and before and after going to my daughter's. But it didn't. It was off by 0.2 lbs in the first case, and 0.3 lbs in the second. That's not huge, but it does highlight just one more source of variation when weighing yourself.

So, this project helps to show the types of variation someone can have in body weight over the course of a day, and the even bigger variation you can get in the weight on the scale depending on the clothes you're wearing at the time, or even how consistent your scale is. If you're weighing yourself as part of an effort to lose weight or to maintain your current weight, keep this in mind as a reason for consistency in when & how you weigh yourself, and as a reason to not worry about small fluctuations.

Related Entries:

Bathroom Scale Image Source:

Updated 2019-03-26: Made a few minor changes to wording to help things read better, but no change to any meaning.

Monday, December 17, 2018

Responding to a Flat-Earther Question: How Much Force Does It Take to Accelerate an Aircraft Sideways as It Flies North-South

In honor of Wright Brothers Day, I'm going to post an aviation-themed entry today. This entry started life as a comment on Quora, in response to a flat-earther. The most interesting aspect of the comment thread was a question the flat-earther raised that I'd never really thought about quantifying before.

If you think about the globe spinning, the equator has the highest velocity, going through one rotation per day. The poles have basically zero velocity, being just spinning about a point (from an earth-centric reference frame, at least).

Earth Rotation Diagram

So, if an aircraft flies directly north-south (or vice versa), in order to remain over the same line of longitude, it's sideways velocity has to change - it has to accelerate sideways*. And that means there has to be a sideways force. Just from experience, you know intuitively that it's a negligible force, but can we quantify that? How much of a force are we really talking about?

The flat-earther actually proposed a good thought experiment to think about the issue. Suppose there were a giant merry-go-round, the same diameter as the Earth, spinning at the same rate of 1 rotation per day. If you started at the center of the merry-go-round, you would have zero sideways velocity. If you walked outward on a straight line painted on the merry-go-round, your sideways velocity would start to increase, keeping matched with the merry-go-round. By the time you got to the edge, your sideways velocity would be quite high - close to 1000 mph.

So, let's actually use the merry-go-round thought experiment to determine the necessary forces. The results will be at least in the right order of magnitude, and it makes the math a whole lot simpler than trying to model all this on a globe.

So, here's a diagram of the scenario. You've got a merry-go-round spinning at some rotational velocity, ω. You have an object moving outwards on that merry-go-round at some radial velocity, Vr. That object, because it's on the merry-go-round, will also have some tangential velocity, Vt.

Figure 1

Our goal is to find tangential force, Ft, which is going to be defined by tangential acceleration, at, so we need to find changes in tangential velocity. So, let's let that object travel for some time, t. In that time, it will cover a certain radial distance, dr, which is obviously just defined by dr=Vr*t.

Figure 2

At the first point, 1, it will have a tangential velocity Vt1, where Vt1=ω*R1. And at the second point, 2, it will have a tangential velocity Vt2, where Vt2=ω*R2. Okay, I think that's got all the definitions taken care of. On to the equations:

R2 = R1 + Vr*t

ΔVt = Vt2 - Vt1
ΔVt = ω*R2 - ω*R1
ΔVt = ω*(R1+Vr*t) - ω*R1
ΔVt = ω*R1 + ω*Vr*t - ω*R1
ΔVt = ω*Vr*t

at = ΔVt/t
at = ω*Vr*t/t
at = ω*Vr

Ft = m*at
Ft = m*ω*Vr

So, things simplified quite nicely, where you don't need to worry about where exactly you are on the merry-go-round. All that matters is how fast the merry-go-round is spinning, and how fast the object is moving radially.

Let's calculate one more value, tangential load factor, nt, which is the g's the object will experience in the tangential direction, and is simply the tangential acceleration, at, divided by the regular acceleration due to gravity on Earth, g. Note that this is only dependent on speeds, not masses.

nt = at/g
nt = ω*Vr/g

Now, let's plug in some numbers, going through an example step-by-step. Let's consider a 200 lb person walking briskly at 5 mph (I'm an engineer in the U.S., so I usually stick with ft, lb, seconds, and the like). So first, rotational velocity, ω, will be one revolution per day, which works out to 6.94e-4 rpm, or 7.272e-5 rad/s. The person's mass is found by converting pounds to slugs, and since m = W/g, we get 200 lb / 32.2 ft/s² = 6.21 slugs. And their speed is 5 mph * 5280 / 3600 = 7.33 ft/s. So, we just plug those into the equations:

Ft = m*ω*Vr
Ft = (6.21 slugs)*(7.272e-5 rad/s)*(7.33 ft/s)
Ft = 0.0033 lbs

nt = ω*Vr/g
nt = (7.272e-5 rad/s)*(7.33 ft/s)/(32.2 ft/s²)
nt = 1.656e-5

To summarize, for a 200 lb person walking briskly at 5 mph, the tangential force required to accelerate them as they walk outwards is only 0.0033 lbs, or 1.656e-5 g's. That force is about equivalent to the weight of 5 staples (according to this discussion, at least). That's really, really negligible.

Let's add a few more cases, but instead of going through all the math step by step, again, let's just put the results into a table.

Person, 5 mph Car, 60 mph 747, 570 mph
ω, rev/day 1 1 1
ω, rpm 0.000694 0.000694 0.000694
ω, rad/s 7.27E-05 7.27E-05 7.27E-05
Vr, mph 5 60 570
Vr, ft/s 7.333333 88 836
Wt, lbs 200 4000 735,000
m, slugs 6.21118 124.2236 22,826.09
at, ft/s² 0.000533 0.0064 0.060796
Ft, lbs 0.003312 0.794974 1387.726
nt 1.66E-05 0.000199 0.001888

Those are all small accelerations, and correspondingly small forces (at least in relation to the size objects). Obviously, the acceleration goes up as tangential velocity goes up, but even at the 570 mph speed of a 747, the radial acceleration is still less than a hundredth of a g.

Granted, the actual magnitude of the force on the 747 looks big enough to be somewhat appreciable, but remember to keep it in comparison to size of the aircraft - 1388 lbs of side force on a 735,000 lb aircraft. To further put the force in perspective, keep in mind that if the aircraft weighs 735,000 lbs, the wings have to create that much lift. So, to get 1388 lbs of side force, the aircraft would have to be banked just 0.11°, since arctan(1388 lbs / 735,000 lbs) = 0.11°. Another way to look at it is in comparison to the engine thrust. Since a 747 has an L/D of around 15.5, that means a drag of around 47,400 lbs, and an equal thrust from the engines to counter that. Even if you completely ignored aerodynamic means of accomplishing the side force, it would mean skewing the thrust just 1.7° off of the flight path. These are very small numbers.

And, keep in mind, we simplified things with a giant merry-go-round, which is actually worse than everywhere on Earth except 2 precise locations. The only locations matching this are at the poles, where the surface actually is perpendicular to the rotation axis. Everywhere else, the surface is more angled relative to the rotation axis. Right at the equator, this force/acceleration drops to zero. All latitudes in between will have force/acceleration values somewhere in between this worst case and zero.

So, an object traveling north-south on a spinning globe does indeed have to have some side force to account for the changing tangential velocity. And while we may know intuitively that the force has to be negligible, it's nice to be able to break out the math to calculate what it would need to be.

Spinning globe image source:
All other diagrams by author


*All this actually applies any time traveling north-south, not just directly north-south along a line of longitude. I was just keeping things simple for the sake of discussion.

Monday, April 30, 2018

Annoyed at Headlines - Star Trek Wasn't Prophetic on Brain Death

Starfleet LogoI know that science reporting ain't what it used to be. And even in the 'old days', when newspapers had decent sized science departments, headlines could be misleading. Still, the reporting on a recent study has irked me enough to become a cranky old man and call it out here on my blog.

Here are a few examples of the coverage. Pay attention to what those headlines are implying.

Here's how Vice summarized the findings of the study.

[Jans] Dreier works at the Charité Hospital in Berlin, one of Germany's leading university hospitals. In February, the 52-year-old and his colleague, Jed Hartings, published a study that details what happens to our brain at the point of death. It describes how the brain's neurons transmit electrical signals with full force one last time before they completely die off. Though this phenomenon, popularly known in the medical community as a "brain tsunami," had previously only been seen in animals, Dreier and Hartings were able to show it in humans as they died. Their work goes on to suggest that in certain circumstances, the process could be stopped entirely, theorizing that it could be done if enough oxygen is supplied to the brain before the cells are destroyed.

About 2/3 of the way through that Vice article, you find the following interview question and answer with the study author.

So how did you find out that an episode of Star Trek had predicted your findings 30 years ago?

My colleague, Jed Hartings, brought it to my attention after watching the scene and noticing how similar it is to our work. My best guess is that the creators of Star Trek must have found research at the time that detailed a similar process in animals. The first person to research these sort of brain waves was a Brazilian neurophysiologist who conducted studies on rabbits in the 1940s. All we've done is show it in humans, which has taken this long because medical research in general is an incredibly slow process.

So in reality, this is a process first studied in the 1940s. The big innovation in this study is that it was done on human subjects, rather that non-human animals, but it shouldn't be a shock at all that human brains function the same as other mammal brains. So, Star Trek's writers back in the '80s were just using an already known phenomenon in their script. You could praise the writers for getting the science right (because they didn't always), but it's not like they made some profound prediction that science is only now catching up with.

All this isn't to say that the new study isn't fascinating. Of course it's interesting to do this study on actual people instead of other animals. But it doesn't sound like it found anything that wasn't already expected.

Image Source: Wikimedia Commons

Monday, February 12, 2018

One More Darwin Day Link

Ape Skeletons

I just came across this article by Scott Solomon, so I thought I'd pass it on:

If you recall, Scott wrote the recent book, Future Humans, so he's in a good position to discuss recent human evolution. Go see what he had to say for Darwin Day.

Image Source: Houston Chronicle

Happy Darwin Day 2018

Darwin's BirthdayToday is Darwin Day, the 209th anniversary of Charles Darwin's birth. To reuse the same thing I've written for a few years now (origianlly here), Charles Darwin was "the man who presented evolution in such a way and with sufficient evidence that it became obvious that it was the explanation for how life developed on this planet. Others had ideas of transmutation before Darwin, and Alfred Russel Wallace even came up with a theory of natural selection very similar to Darwin's at around the same time, so it's apparent that humanity would have eventually recognized how evolution works. But Darwin's genius in presenting all the evidence for evolution in the way he did certainly gave the field a huge head start."

Although Darwin Day this year isn't getting anywhere the same attention as the bicentennial of Darwin's birth a few years ago, there are still Darwin Day events at various locations. If you want to see if there's anything near you, you can check out the list of events at (I checked there and local calendars, but couldn't find anything for today in Wichita Falls.)

To celebrate Darwin Day on this site, I just posted a new entry today giving a concrete example of speciation:

Since the last Darwin Day, I've also created a section on this site highlighting some of my better writings on evolution, as a starting point for people who may not understand it very well. There are actually several entries there that are new since Darwin Day last year, so go check it out.

And here are a couple more entries I've written about Darwin that are appropriate for today.

Finally, here are links to external sites with good information about Darwin and evolution. The first is brand new this year, the next two are from the bicentennial celebration a few years ago, and the last is just a classic that's been around for years.

  • Oxford University Press - Darwin Day 2018 A great collection of links to articles and resources about Darwin.
  • Nature's Darwin 200 The prestigious journal has put together a collection of articles, editorials, news stories, and various other essays and features that have to do with evolution in general or Darwin in particular.
  • American Museum of Natural History's Darwin page Yet another good collection of information. This is from the exhibit that ran in the museum from 2005 to 2006.
  • The TalkOrigins Archive Has a bit more focus on the creation/evolution controversy rather than just straight science, and hasn't really had too many recent updates, but it is still very, very informative.


Selling Out