Examples of Applied Physics

[Justin Adams]

9 hours ago, GandalfTheWise said:

I was rather curious to see how atmospheric pressure changes with altitude and how that compared to actual weather data.

I use Mathematica for much of my professional work.  See wolfram.com for more details on it.  It is a powerful mathematical package with a lot of curated data and information built into it.  I used their built in standard atmosphere functions, weather data, and city information to generate an interesting graph showing how the earth's atmospheric pressure changes with altitude.

The blue line shows the 1976 version of the US Standard Atmosphere Model.  This model gives what is essentially the average value of temperature, density, pressure, and other quantities at various altitudes in the atmosphere.  It is used for aircraft engine design, ballistics, and other applications where various properties of the atmosphere are important to know at different altitudes.   This model assumes that the atmosphere is dry and there is no wind or other such effects.  Users of the model must add the effects of wind, water vapor, precipitation, and other such things themselves.

Various sites on the web have more information about this model.  The wiki page isn't too bad of a place to start. https://en.wikipedia.org/wiki/U.S._Standard_Atmosphere

The red line shows the estimated effect of water vapor in the atmosphere.  This is a very complicated type of interaction that has different aspects of things to consider.  The main thing to know is that it will reduce the atmospheric pressure by a few percent or more depending on temperature, dew point, and other things.  The red line is set to a 5% reduction to provide a reference point for the city information.

The 4 cities give the average raw atmospheric pressure measurements over a 2 year period from 9/10/2015 to 9/10/2017.  I pulled this in from the Mathematica weather data set.  As can be seen, they all sit a few percent below the dry atmosphere pressure curve as would be expected.

Is that how Density Altitude is calculated? It appears to be most critical as temperature rises and the 'actual' performance (air craft) altitude come into play. For an airplane, that can add 1000 feet to the takeoff run for a given 'book altitude'. Depending on the temperature and a few other variables, Density Altitude may be actually above the Service Ceiling of you particular air craft. Most noticeable in rotary craft I am told.

[bryan]

Fascinating stuff here.  When I was flying small planes in Colorado the rule was that temperature, pressure, and even humidity all are part of what determines whether it's safe to take off.  It's counter intuitive to me, but days with high humidity where the air 'feels think' are actually worse days for flying.  I'm told it's something with the water molecules being larger and the wings having less to 'grab'.  That's just what I remember from a long time ago, so please correct as needed.

[GandalfTheWise]

1 hour ago, Justin Adams said:

Is that how Density Altitude is calculated? It appears to be most critical as temperature rises and the 'actual' performance (air craft) altitude come into play. For an airplane, that can add 1000 feet to the takeoff run for a given 'book altitude'. Depending on the temperature and a few other variables, Density Altitude may be actually above the Service Ceiling of you particular air craft. Most noticeable in rotary craft I am told.

Cool question.  My first thought was, "I've never heard of density altitude."   Instead of giving my final answer right away, I'll use this post as an example of how I figure something out when I've never heard of it before.

The first thing I did was use Bing to search for the definition.  I used wiki and aopa.org sites to get the definitions.  Sometimes this can be a chore sorting through people's attempts at an explanation (which may or may not be completely clear or accurate).  The AOPA site was fairly clear and also gave the formula for pilots to use.  I found this very useful since it's what people use in practice.  From this, I was able to relate what was happening to my general knowledge of thermodynamics and mechanics.  I'll try to answer this now in a way that non-pilots can follow.

An airplane can fly because air pushing against the bottom of the wings causes enough upward lift.  It's more complicated than that, but this basic idea covers most of what you need to know.  The amount of lift generated depends on many things.  The faster the plane is moving the more lift.  The shape and angle of the wings affect the amount of lift.  And most importantly for this example, the density of the air affects the lift.   Very dense air (like at low altitudes) has many more atoms and molecules per cubic inch (or whatever volume you with to use) than less dense air (like at high altitudes).  The more atoms and molecules striking the bottom of the wings, the more lift.  This is why different types of aircraft have different limits on how high they can fly.  Depending on the aircraft design, it will need more or less air density to properly operate.  The amount of lift also affects take-off and landing distances!  Taking off from sea-level is much different than taking off from an airfield in the Himalayas.

There are 3 main factors that go into how dense the air is.  These are altitude, temperature, and humidity.  A lot of work has been done on the standard model of the atmosphere.  Here is a graph I generated using Mathematica.  It shows the 1976 US standard atmosphere model (which assumes a dry atmosphere at standard atmospheric conditions).  In other words, this is basically the average density of air for a dry atmosphere at a given altitude.  The blue line shows the density at altitude for standard dry conditions.  However, higher humidity and temperature cause the density to decrease.  I put in a random red dashed line to indicate what this might look like.

So, if an aircraft requires at least 0.8 kg/m^3 air density to fly, under ideal conditions its maximum ceiling would be about 15,000 feet.  On a hot and humid day, its maximum ceiling would be more like 10,000 feet.  (It's really much more complicated than that, but this gives the general idea.)

In practice, pilots do not directly use this type of graph.  A pilot doesn't want to know if the air density is 1 kg/m^3 or 0.5 kg/m^3.  What a pilot wants to know is what the equivalent altitude is that they are at.  Density altitude is a simple formula that takes a measured pressure altitude reading and measured temperature reading and indicates what the equivalent altitude is.  It is basically a way of taking the altimeter reading and saying "your plane will behave as it would XXX feet above what the altimeter says."  

[GandalfTheWise]

1 minute ago, bryan said:

Fascinating stuff here.  When I was flying small planes in Colorado the rule was that temperature, pressure, and even humidity all are part of what determines whether it's safe to take off.  It's counter intuitive to me, but days with high humidity where the air 'feels think' are actually worse days for flying.  I'm told it's something with the water molecules being larger and the wings having less to 'grab'.  That's just what I remember from a long time ago, so please correct as needed.

Higher humidity air being less dense seemed pretty counterintuitive to me too.   When I first started researching things for this thread I ran across that and thought "What?!?".   Air is mostly nitrogen and oxygen molecules, which are N2 and O2.  The atomic mass of N2 is about 28 and O2 is about 32 whereas water H2O is about 18.  Water molecules are much lighter than N2 and O2 molecules.  A given container full of N2 and O2 will be heavier than the same container full of N2, O2, and H2O.  At least, that's the way I think about it now, and it seems to match what is observed.   

There's stuff about partial pressures and how different species of molecules interact in fluids that I haven't looked at in ages that has something to do with this as well.

 

[hmbld]

40 minutes ago, GandalfTheWise said:

The more atoms and molecules striking the bottom of the wings, the more lift.  

I was taught if wings on birds or planes were configured this way, drag is increased. However, if the bottom of the wing is fixed more flat in relationship to air passing, and the top of the wing is curved, creates a longer path for air to travel over the wing, creating a lower pressure, in effect, lifting from above the wing, not below it.   More efficient as drag is reduced. 

[Justin Adams]

Yes. Higher humidity can be a killer for two reasons. Volumetric weight is less (mass), and icing due to the dew-point spread being that much less than dryer air. For normally aspirated engines the volume is a concern, for turbo fuel injected engines not so much. Carburation (normally aspirated) depends on a given volume ratio (slightly variable via the mixture control), whereas injected engines have fuel pressure regulators than can be adjusted based on the EGR (exhaust gas temperature) gauges and flow adjustments based on mass (weight). Turbos do not have so much of a problem, like if you have a car with a turbo charger. The turbo crams more air (mass) into the engine, so more fuel can be added and an increase in HP can be realized. (Hope I got this all correct - it has been 40+ years ago).

[GandalfTheWise]

Since I had Mathematica up and running and playing with the atmosphere model, I decided to put out a graph showing the temperature model.  I added the blue, green, and red bands show the troposphere, stratosphere, and mesosphere.   The straight line segments (rather than smooth curves) are because the model is focused primarily on quantities like density and pressure which are what pilots and other uses of the information need the most.  The temperature is shown as linearized between important inflection points (e.g. the top of the stratosphere) and is primarily used to generate smooth density and pressure information.

 

Notice how cold things get very quickly as you go up.

Notice that the ozone layer in is the stratosphere.  Ozone absorbs some energy from the sun and causes warming in the upper atmosphere.  Without the ozone layer, the temperature would continue to drop.  Without the ozone layer, the stratosphere really wouldn't exist.  This has a profound effect on our weather.  This temperature peak is what stops warm air masses from rising indefinitely.  It basically puts a cap on how high warm humid air can rise and how high thunderstorms can build up.  Here's a great image from wiki showing this effect.  (original link to full size image: https://commons.wikimedia.org/wiki/File:Single-cell_Thunderstorm_in_a_No-shear_Environment..jpg)

 

 

[other one]

4 hours ago, Justin Adams said:

OK. Well it is 1974 and we are going on a trip from Edmonton to Yellowknife. You fly - I'll watch.
I'll let you do the flight planning as well. Here are some reminders. 
Since it is Sparsely Populated Area, we will need the emergency gear. We will stop on the way to refuel. The Arrow burns about 8-10 GPH (check if that is Imperial or USG). Make a note of the following frequencies in the log:
GRND here, TWR here, and at destination. Transponder freq(s). Departure and Term. Area freq, plus the military base tower we will pass just to the north. We'll give them a courtesy call on the way by. 
Be sure to list on our preflight a check using the local VOT and local NDB. VOR is needed to get a fairly good initial heading, but the NDB will be our main X-Ref Nav-Aid until we get closer to the destination. Since our plane only had one NDB, we need all the freq. listed for easy ref. So make a note also of en-route radio stations we can fix on. Check the ELT. 
It will be a normal VFR dead reckoning flight so the winds aloft are important along with the weather. We can check the automated weather reports on the way.  Because it is minus 30F right now, the lapse rate means it will be colder up there. Verify the Dew Point Spread along the route. Decide on a legal altitude and compute ETA, ETE, CH, (for both legs) and estimated Ground track (don't forget the deviation) and fuel needed per leg. Mark the course on the sectional chart. As we go we can check actual GS and track and make any necessary adjustments. You can go and do the pre-flight and check for any PIREPS, NOTAMS etc. TimeAir does the trip a lot so they will update the winds if they are different than the forecast. 
We will probably encounter White-Out conditions nearer the destination, but since it will be getting dark by then, a few lights on the ground will give us a better visual reference. Don't forget the cockpit  flashlight! We will have Yellowknife Radar give us a DF steer when we get closer - they like the practice. We dont have DME capability, so  Radar is normally glad to help and give us a precise location and track.
Do not forget to CLOSE the flight plan when we arrive. Wear your woolens. Off you go and do the weight and balance when you have got the fuel calculated. Remember we have the extra weight of the mandated emergency gear in back. You do the walk-around and don't freeze!
One last thing before we fly during run-up. Double-check the ELT is not broadcasting - we don't want SAR after  us before we even take off! 
The way the pilots here bounce these planes around, sometimes they set off the ELT. 

none of that is difficult but the landing and that's why they bounce the planes around.....    and we have checklists to make sure we don't forget anything....     but landing takes some skill and practice.

[Justin Adams]

Checklist are OK. for takeoff and landing. And perhaps cruising (without a flight-commander).

However, the bit in between can be long periods of boredom, punctuated with short, sharp periods of extreme terror.
I have a few stories about those in-between periods that still make me sweat.

A great place to learn how to land I found at Redbird, Texas (not far from Waco). Try there when the winds are squirrely; In March-April; they veer and back continually and wicked crosswinds are the norm.  If you just keep trying to drive onto the asphalt, eventually your senses and autonomous self-preservation instincts allow you to survive. Building a kind of feeling that you are actually 'wearing' the airplane, and not just operating it. It does take practice as you rightly say, but not mental practice only. You, as an extension of the machine, fly onto the ground. Watch a pigeon on a blustery day manage to land on a branch that is moving. 

[GandalfTheWise]

2 hours ago, hmbld said:

I was taught if wings on birds or planes were configured this way, drag is increased. However, if the bottom of the wing is fixed more flat in relationship to air passing, and the top of the wing is curved, creates a longer path for air to travel over the wing, creating a lower pressure, in effect, lifting from above the wing, not below it.   More efficient as drag is reduced. 

I used to take this as the standard explanation.  I now think it is a "truth by repetition" situation.  Many years ago I was helping a colleague study for his pilot's license.  He kept asking me questions about stuff like this.  At first, I just repeated the standard answers until I realized I really didn't understand how angle of attack, Bernoulli's equation, and simple force diagrams applied to flight.  I then realized I could not explain how aircraft can fly upside down.   I went back to first principles and finally came up with some reasoning that I was comfortable with.

1. Air is a fluid.  It cannot pull outward on anything, it can only push.  (Strictly speaking, it can cause shear forces to the side for objects with rough surfaces.  But this is really just pushing against the rough projections.)  It is the pressure differential of high pressure under the wind and low pressure over the wing that causes a net force upward.

2. Bernoulli's equation does NOT dictate cause and effect.  It merely states that high pressure is associated with low air speed and low pressure is associated with high air speed.  In some cases, pressure differences can cause air to move.  In some cases, air being blown into an object slows down and builds up pressure.

Here are a couple crude schematics I just tossed together to illustrate this.  In the top case, a fan starts to blow air into an enclosure.  The arrows show the air speed and the coloring shows the pressure.  When the fan is turned on, the air rushes into the box and is stopped by the far wall.  The pressure build up against the back wall stops the air.

In the bottom schematic,  the fan is turned off.  Air then starts to rush out of the box.  The higher pressure near the back wall is pushing the air out of the box.

 

Here is how I think of a wing in terms of cause and effect of pressure and air speed.   Moving air (from the forward motion of the plane) piles into the bottom surface of the wing (which is angled upward slightly called the angle of attack).  Because of the angle of attack, the air is striking the bottom of the wing and producing a region of high pressure where the wing stops the air.   This builds up pressure causing the pressure under the wing to be higher than pressure over the wing.   The primary effect of the rounded shape of the wing is to reduce turbulence and drag not produce a pressure difference.

Now, imagine if the standard "Bernoulli" explanation of cause and effect was correct.  What would happens when flaps or ailerons are used?  If the "Bernoulli" explanation of air traveling faster and farther causing low pressure was correct, they'd be working backwards.  Lowering ailerons would cause the air to have to travel further and faster reducing pressure and causing a wing to drop if an aileron or flap was lowered.   But, if the cause is the moving air pushing into them building up pressure, they work as expected.

I think it is much more intuitive and accurate to think of air movement pushing against the aircraft wings to figure out what is happening.  I think that someone somewhere misapplied cause and effect in the Bernoulli equation and got the cause and effect backwards.

Also, if the wing shape causes lift rather than air pushing on the bottom of the wing, the old rubber band wooden airplanes I used to have as a kid would not have worked as well as they did.    Those were nothing more than cheap flat stamped wood.  Here's an image I found.  I recall mine had cheap wires and little plastic wheels for landing gear.  It was fun winding them up, setting it on the ground, and then watching it take off.

If someone has further info on this,  I would be willing to reconsider my position.  But thinking about things this way made it easy to answer my friend's questions about various things and he (an engineer) seemed to think that my explanation made a lot more sense than what he was reading and being told.

Edited September 24, 2017 by GandalfTheWise
Added a sentence I forgot.