Can an airplane take off on a treadmill going as fast as the top speed of the aircraft?
The answer to the question is yes, but that’s not the interesting part. The interesting part is the explanation, which is notoriously difficult.
Airplanes take off by moving forward first, then up. They don’t take off right away; this is why runways are so long. So to simplify the original question, let’s ask “Will a treadmill stop an airplane without wings from moving forward?”. To stop the plane from moving, the frictional force from the treadmill acting on the wheels pushing the plane backwards must equal or exceed the thrust of the engines pushing the plane forward.
Aircraft engines don’t push on the ground to generate movement, like cars do. They push on the air. Obviously, when you’re flying, there’s no ground to push on, so this has to be the case. So with or without wheels, an aircraft’s engines will push the plane forward.
Airplane engines generate a tremendous amount of thrust. Keep in mind, they are designed to take a vehicle weighing several tons and throw it through the air at 500 mph.
Watch this video to get an idea of just how powerful jet engines are:
How much force does a treadmill exert?
Aircraft wheels are free spinning. When an airplane lands, the wheels go from stationary to 200 mph in a fraction of a second. If they were not extremely low friction, they would be ripped off. An airplane’s engine doesn’t connect to the wheels in any way. They are more like a skateboard or a furniture dolly than a car.
Suppose someone took a small airplane and put it on a treadmill and then tied a rope to its nosecone and handed the other end of the rope to a normal human being.
If the treadmill were slowly brought up to speed, could the human hold on to the rope? They’d have to pull a bit, but they could hold it. Now try the same stunt with a car and their arm would be ripped off.
So, we have a huge force pushing the plane forward and a tiny force holding it in place. According to the laws of physics, if you have a net force applied in one direction, acceleration will occur. The plane will move forward.
Theoretically, if the treadmill were moving at an insane speed, like 2,000 mph, the friction from the wheels might generate enough friction to substantially slow the aircraft’s acceleration. However, at the speeds where friction would generate substantial amounts of friction, the wheels would melt and the landing gear would rip off and the plane would be torn apart by the insanely fast treadmill beneath it. Landing gear is not strong enough to hold together against the forces the engines can generate.
Now that we’ve established that the plane moves forward, it will eventually reach the critical speed, and the lift from the wings as well as the thrust from the engines will push the plane upwards. The faster the plane moves, the less its weight pushes down on the runway, and the less friction the wheels will generate.
Reducing the problem down to whether the plane moves forward makes it much easier to solve and sidetracks any nonsense about lift or airflow or anything like that.
The Mythbusters actually tested this, so if you just want to watch a video as proof, here you go:
Note: The capital in the title refers to institutional capital at central banks, but I wanted alliteration more than clarity.
Imaginary conversation between two economists:
Naive Economist: Wow, what the central bank was tremendously stupid. It caused price instability, high unemployment, and financial instability.
Worldly Economist: Ahh, but the central bankers are building institutional capital.
Naive Economist: But can’t they do that by providing stability and doing what they say they are going to do?
Worldly Economist: No, they have to do stupid things that destroy the economy.
Naive Economist: Oh, that makes sense.
In any other profession, incompetence would be called incompetence. Maybe it’s because macro is so cloaked in obfuscation that everyone just assumes that what the people in charge do is right, regardless of their consequences. There is no wizard behind the curtain. People with power aren’t super smart or know things no one else does, they are just people who make mistakes like the rest of us. But if the mistakes aren’t pointed out and corrected, they will just continue.
The Swiss Franc appreciated about 20% a couple weeks ago when they went of the Euro peg. That’s an insane fluctuation for a currency in a single day. Ideally, currencies should change less than 5% in an entire year. To change in value 20% in a day is prima facie evidience that someone at the central bank screwed up. Big time. Swiss equities dropped about 10% on the news that the Swiss National Bank was going to abandon their currency peg with the Euro.
That doesn’t bother me. Central banks do stupid things all the time. The ECB has been riding the moron train for the better part of a decade now, so no big deal right? What bothers me is Tyler Cowen’s reaction to it. He posits three possible explanations, which I have excerpted below:
1. “Bureaucrats are not so much budget maximizers as hoarders of institutional capital.”
2. “They either cannot do “the right thing,” or doing that would be too costly in terms of the country’s longer-term institutional prospects.”
3. (which Tyler does not find credible) “The Swiss central bankers suddenly became stupid and forgot their macroeconomics.”
1 and 2 both rest on the assumption that bad policy is good politics. I guess that makes some sense to me. Deflation is highly popular with some Republicans these days. If they had their druthers, I can imagine them putting tremendous pressure on the central bank. I know very little about Swiss politics, so perhaps it was political pressure that forced the Swiss National Bank to abandon the peg.
But I think in those cases, it’s the central bank’s duty to at least pitch a fit. Tell people that’s why you’re doing the stupid thing. “Guys, this is a bad idea, but if that’s what you want…” No one should be wondering why things went wrong afterwards. As an added bonus, this discourages politicians from pressuring central banks.
It can be hard to judge central bank actions as they are happening, but are there any examples from history where a central bank deviated from price stability and was later vindicated? Maybe, but no examples spring to mind. The Great Depression looks like #3 to me, as does the period of 1970s inflation. Is the argument that #3 may be common in the past, but not anymore?
Everyone is rational, but that does not mean their actions are not stupid in the broader sense. A criminal may rob a bank which is rational, but as a society we do and should wring our hands to figure out ways to prevent that from happening. Pete Leeson has written some fascinating papers showing how a wide variety of seemingly crazy behavior is actually rational in the microeconomic sense. I suppose I could be convinced that the bureaucrat’s actions are narrowly rational, but that does not mean economists should not call them out. When a thief robs a bank, normal people understand that it is harmful to society as a whole, but if a central banker screws things up, people won’t actually know that it was bad unless other economists call them out.
Credibility and Time Consistency
Time consistency sometimes rears its head as a reason why central banks must do stupid things from time to time. Just to get it out of the way: I don’t think past central banks can bind future central banks. But I don’t think there is any sane target which requires them to do so. If you want to target inflation, just target inflation in every time period. As long as the target itself is politically popular and the economists deems it reasonable, Bob’s your uncle.
Central banks mostly spend institutional capital defending themselves in the wake of their own screw-ups. Imagine a central bank that held inflation at 2% and has done so as long as anyone can remember. What, precisely, would such a central bank need institutional capital for? It’s not until they have a year with 10% inflation that they need institutional capital to convince people they’ll get it right in the future. Is it radical to suggest that a central bank should gain institutional capital when it does good things?
Where do we go from here?
This is where the economics profession has a role to play. We must not let central bankers get away with bad decisions and say “maybe they had a secret good reason for it.” I agree with Scott Sumner (I can’t find a link) that central banks generally go with the mainstream opinion for macroeconomic policy. If 90% of macroeconomists agree with a policy, that’s what they’ll do. But if we let them get away with it, they’ll never learn.
Cowen on why the Swiss broke the peg
Sumner calls it how he sees it
Francis Cappola on how bad breaking the peg was
Maybe it was for balance sheet reasons. Sounds like a good argument for nationalization to me. A central bank shouldn’t care what its balance sheet is.
2. Japan Photo essay. Very much makes me want to go back. I visited several of the places pictured, and their spirit is captured very well.
3. Running for your life from Shia Lebeouf. Your daily dose of WTF and then some.
UPDATE: Big news
5. Federal Asset forfeiture program dealt a huge blow!
This post is for Update 15.8. I do not intend to update this post for newer versions of Warframe.
Warframe has had a serious balance problem throughout its history. Balance isn’t about having all weapons about the same power level. Balance is about introducing meaningful choice into which weapons are good. It means that advantages are matched with disadvantages. Ideally, the balance would be so good that the most popular article on this blog would be impossible to write.
Starter weapons should do less damage than MR 0-2 upgrades, which in turn should do less damage than primes and high MR clan-tech. I sorted weapons into 4 tiers: Starters, Basic, Advanced, Primes+. Starters have MR 0-2 and are not difficult to acquire. Advanced are either low-MR clan tech, medium clan tech, non-Wraith/Vandal event rewards, or some factor which makes them hard to get. Primes+ are weapons that are either Primes, Wraiths, Vandals, Dragon, or MR 6+ Clan tech.
Starter weapons get a DPS penalty of 20%, Basic weapons are 1.0, +20% for Advanced, and +40% for Primes+. That way, hard to get weapons can do more damage and still be considered balanced.
Faster weapons should do less damage. This is because with melee, the initial time before the enemy takes damage and is staggered is very important. Rapid attacking weapons have a major advantage over slower weapons beyond the mere fact of thereby being able to do more damage. Berzerker is more likely to trigger with a fast attacking weapon, as are status effects. I assigned a factor of (2.-attack speed) to DPS. This means that a weapon with an attack speed of 1.3 will get a DPS factor of 0.7, and a weapon with a 0.7 attack speed will get a factor of 1.3.
Small AOE weapons such as Sparring and Daggers should get 10% more DPS to compensate, and Large AOE weapons such as polearms and heavy weapons should get 10% less DPS to compensate.
The average base DPS of all WF melee weapons is 54.86. I started with a base DPS of 50, applied my modifiers above and got an average of 56.5 if the weapon damages were changed to what I think they should be. That’s a bit of a buff, but close enough. I think in any rebalancing effort, the average damage should increase, since the unbalance is mostly caused by the OP weapons being too good rather than the bad weapons being too bad. If a weapon is bad enough, people will simply ignore it, or passively level it and sell it. However, overpowered weapons show up in every match and have a huge impact on the game. The average weapon damage could increase by 50% and still the average weapon DPS for weapons actually used in game could decrease. Perhaps an increase to an average of 60 or 70 would be acceptable. Either way, the ranking is unaffected by the scaling anyway.
25 most underpowered weapons
Large buffs needed:
Ether Daggers 0.434848485
Plasma Sword 0.433461538
Fang Prime 0.479220779
Dark Sword 0.505666667
Pangolin Sword 0.517159091
Dark Dagger 0.533677686
Dual Skana 0.546666667
Heat Dagger 0.559090909
Silva and Aegis 0.597916667
Slight buffs needed:
Skana Prime 0.615
Ceramic Dagger 0.652272727
Dual Cleavers 0.583333333
Prova Vandal 0.702857143
15 most Overpowered Weapons
Name Overtiering factor
Large nerfs needed:
Galatine 2.546296296 – If the damage is nerfed a bit and the current damage is used as it’s charge attack damage, that would balance this weapon. It’s mostly too fast right now. If the speed were dropped to 0.8, it would be fine.
Tipedo 2.476190476 – Like the Galantine, it’s just too fast. 1.3 is extremely quick for a basic tier, 50 damage weapon. Raise the MR to 5, put it in the Tenno Clan Lab, drop the speed to 1.2 and it’ll be fine.
Scindo Prime 2.476190476 – Not surprising that the highest DPS weapon in the game makes the OP list.
Jat Kittag 2.373015873
Slight nerfs required for weapons below this point:
Orthos Prime 1.702380952
Bo Prime 1.636904762
MK1-Bo 1.40625 – Surprised a MK1 weapon made the list?
Dragon Nikana 1.396428571 – Not actually that bad considering the MR of 8. It really should be one of the best weapons.
Whenever you get riled up about some injustice, it’s always useful to step back and ask “how important is this?”. Otherwide, you spend your time worrying about plane crashes and terrorism rather than heart disease. Police brutality is to the left what terrorism is for the right. It kills very few people, but triggers a strong emotional reaction. Because I follow many anarchist-leaning libertarians on Twitter and Google+, I see stories of police brutality nearly every single day on my social media feed, so it has a really high salience for me. But is it a major problem?
In total, in the U.S. there are around 16,000 homicides per year. There are about 1,000 people killed by police per year, so it’s not a major cause of death. According to the FBI’s report, about half of those are justifiable homicides. So unjustifiable homicides by police are about 3% of all homicides. Higher than the general population, but not a major cause of death. I realize these numbers are extremely rough, but they are to provide orders of magnitude, not exact statistics.
Source: Washington Post
Why is Police Brutality such a Faultline?
According to Kling’s Three Axes Model, conservatives frame issues on the Civilization/Barbarism axis. Things which support the orderly functioning of civilization are good, things which disrupt civilization are bad. Progressives frame issues in terms of Oppressors/oppressed. Those who oppress people are bad, the oppressed are good. When the defenders of law and order start oppressing people, get ready for some fierce political bickering.
Using Haidt’s 6 factor Moral Matrix, conservatives emphasize Sanctity, Loyalty, and Authority, whereas liberals emphasize Care and Fairness. To a conservative, we should be loyal to the police and respect their authority. Liberals focus mainly on the unfair treatment of minorities and the harm that that causes.
There are other philosophical objections. Cops are supposed to be upholders of the law, so they should be held to a higher standard than normal people. The legal system is biased in favor of police, and if you give someone impunity, there should be some other constraints to make sure they don’t run amok. I don’t think it’s healthy for any society to have a large group of people who are above the law.
Cross country comparisons
The vast majority of first world democracies have basically no one killed by police, except in extreme countries: Scandinavia, Britain, New Zealand, Australia, Canada, Western Europe, Japan all have very low rates of police homicide.
On the other side of the equation, you have places like Russia and China. The Russians kill journalists, dissidents, and Chechens with gusto, yet still report American police’s bloodlust with glee. The one shining star of Russian journalism is pointing out Western hypocrisy.
I’d prefer the U.S. to be with the other well functioning democracies. It’s certainly possible. I don’t buy the gun culture argument either. Canada and Switzerland have high gun ownership rates and their police aren’t very violent. Some combination of body cameras, accountability, and culture change would probably drive violence by police and against police down. It’s important to note that violence by police has been trending downward, so the situation is far from hopeless.
Why are the American police more violent than other rich countries?
The drug war is probably the single biggest factor. Other types of crime have a victim, someone to alert the police to the fact that a crime has been committed. Even something as trivial as littering produces publicly observable evidence of the crime. Drug use is the one of the few crimes where everyone involved doesn’t want the police to find out. Even people who desperately want the drug users to stop using drugs, such as family members, want to conceal drug use from the police because the severity of the punishment. A mother who catches her teen using pot should be as terrified of the police as the teen, because she doesn’t want her child to spend the next decade in prison surrounded by violence criminals.
The stealthiness of drug users needs to be paired with an equal inquisitiveness on the part of police for the drug war to be remotely effective. The drug war has led to warrantless searches, asset forfeiture, no knock raids, and general corruption of the entire law enforcement system. Without the drug war, the necessity of the degree of law enforcement present in our society evaporates. Cops would be left to enforcing laws with actual victims, which are far fewer in number.
Any time you have a law, that law needs to be enforced, and any interaction with the police involves some risk of death, both for the police officer and the citizen. So, I think the criminalization of everything is an unhealthy trend, especially with pervasive surveillance. If everyone is a criminal, and the government can prove it, they still aren’t going to actually arrest everyone. But they could arrest anyone. That leads to corruption and politically motivated law enforcement which is troubling in a democracy. I don’t think it’s unreasonable to say that the law should be such that less than 10% of the population are criminals.
Culture and Racism
One of the questions that people seem very concerned about is whether or not the police are racist and whether or not the legal system is biased against African-Americans. There’s a lot of evidence for that hypothesis. While African Americans comprise 12.6% of the population, they make up around 40% of the prison population. While the various races have similar levels of drug use, African Americans are about three times more likely to be arrested for drug use. African Americans are more likely to have violence used against them by police as well, satirized by the Twitter hashtag #crimingwhilewhite.
But like any empirical issue, it’s complicated. If you account for poverty and education level, and a ton of other stuff, the legal system starts to look less racist, but then again it may not make sense if racism is the reason for the variables you are using as controls. I’m not an expert on this issue at all, but it does seem like African Americans are targeted by police violence more often.
If you know that, in general, your race is frequently on the receiving end of police violence, it makes sense to be overly polite toward cops. Some cops freely admit that they will hurt you at the drop of a hat. When you are interacting with a cop, remind yourself that it is a possibility that on the job violence is the reason why they took the job. Don’t mess with them. Know your rights. Keep your mouth shut. Follow directions. If you think they are doing something wrong, hire a lawyer and fight it in court.
In an ideal world, there would be far fewer interactions between police and citizens where either of them feared for their lives. We don’t live in that world, but we’re getting there.