# An air density puzzle

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Here's a little puzzle to divert you attention for a while.

There are two identical sailing ships. Their masses and rigging are exactly the same.

One of the two is sailing from the Alaskan island of Kodiak (58 degrees North), while the other is sailing from Mackay, Queensland (21 degrees South)

If both ships have a direct tailwind of 10 knots, which ship will be expected to go faster? (disregard the effects of water density)

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Relativistic effects and varying density of the earth and gravimetric effects included or disregarded ?

Edited by RFguy
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You would have thought the denser air in the colder spot would have more push?

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2 minutes ago, RFguy said:

Relativistic effects and varying density of the earth and gravimetric effects included or disregarded ?

What about the Coriolis force? 😁

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Neither. If the wind is measured at 10 knots then the same number of molecules are hitting the sale area per sq meter with the same force. 10 knots is 10 knots using anemometer. So it’s going to come down to the captains ability.

Edited by Jase T
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I think hot and humid  in Mackay and cold and dry  at the north pole is a good assumption.

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1 hour ago, RFguy said:

Relativistic effects and varying density of the earth and gravimetric effects included or disregarded ?

Short run length, say 10 Nm should allow those to be ignored.

1 hour ago, Student Pilot said:

Ditto

1 hour ago, Jase T said:

at 10 knots then the same number of molecules are hitting the sale area per sq meter with the same force

A flaw in my otherwise flawless conditions. However, from here on in, I will specify that the wind speed is measured by a hot-wire anemometer. They take advantage of the fact that air cools a heated object when it flows over it. In a hot-wire anemometer, an electrically heated, thin wire is placed in the wind. The amount of power needed to keep the wire hot is used to calculate the wind speed. The higher the wind speed, the more power is required to keep the wire at a constant temperature.

Just to eliminate two more variables, let the humidity and air pressure be the same for both ships.

I will say that Student Pilot and Jase T are thinking along the same lines as I am. They just need to expand their replies to give their reasoning.

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Instead of confusing us with the hot wire anemometer will a balloon at both locations travel 10 nautical miles in one hour? The only reason I ask is because the hot wire anemometer sound like a mass flow sensor in a efi engine.

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What nationalities are sailing the boats.

Any sailing boat crewed by New Zealanders is going to have an advantage 😁

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Yes. A balloon, within an air mass is stationary relative to  it. If the air mass moves at 10 kts, then the balloon will move at 10 kts in the direction of the wind flow.

Why can't people accept, for the purposes of the simple exercise, that the air mass adjacent to the ships is moving at 10 kts from directly astern and leave it at that?

3 hours ago, Thruster88 said:

the hot wire anemometer sound like a mass flow sensor in a efi engine.

I don't know, and, frankly my dear, I don't give a damn!

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17 hours ago, old man emu said:

Here's a little puzzle to divert you attention for a while.

There are two identical sailing ships. Their masses and rigging are exactly the same.

One of the two is sailing from the Alaskan island of Kodiak (58 degrees North), while the other is sailing from Mackay, Queensland (21 degrees South)

If both ships have a direct tailwind of 10 knots, which ship will be expected to go faster? (disregard the effects of water density)

You could simplify the whole question...take two identical kites each in the locations mentioned. Tie the strings to a calibrated spring balance.  Which one would be pulling harder in a steady ten knot breeze ?

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4 hours ago, lee-wave said:

You could simplify the whole question

I should have simplified the whole bloody thing by not posing the question at all. I pose a serious question and get stupid responses. There are times and places for wit and repartee. One of these is called socialaustralia.com.au.

The point of the question, and, dare I say, the title and location where it exists, indicate that it is something to be contemplated in light of pilots' supposed knowledge of the properties of the atmosphere and the effects those properties have on Man and machine.

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Theoretically, the Alaskan Ship will accelerate faster as the air would be more dense (assuming the air temperature in Alaska is colder than the air temp in Airlie Beach).

For a given volume, the air will have a higher mass and therefore a higher kinetic energy, which is passed on to the ship.

The maximum speed will be limited to 10 knots though, they are not going to go faster than the wind running dead square, so it's possible they end up at the same speed.

This also assumes that they are longer than 55 feet. If less than 55 feet, they will be limited to their hull speed, which is a function of waterline length.

The Alaskan Ship will also have less drag as the water is more dense, so it will displace less volume for the same mass, thus have less hull surface in contact with the water.

Edited by RossK
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Yep. Like that explanation.

At sea level, air density at 10C is 1.2466 kg/m^3 , while at 30C it is 1.1644 kg/m^3. The cold air is 7% denser. I was thinking along the lines of Conservation of Momentum in a collision. In this case, the collision is that of a cubic metre of air colliding with a square metre of sail. You would have to work out the area of the profile of the ship (sails and exposed hull) to work out how many cubic metres of air are colliding with the ship and from that, the mass of the air striking the ship. You also have to assume that all the mass of the cubic metres of air is in the square metre that first meets the ship. (Think of an infinitesimally thin wall having all the mass of the cube). 10 kts = 5.1 metres per second

From the Law of Conservation of Momentum:

mair1 x vair1  + mship1 x vship1 = mairvair2 + mship2 x vship2

When the cubic metre of air collides with the ship, the wind is stopped. Therefore all its momentum is transferred to the ship, resulting in an increase in the velocity of the ship.

This question has not raised the point that RossK alluded to in that with denser water there is less hull on the water, hence less Drag. So in colder water, less of that velocity change is lost to drag that would be the case in hotter water.

RossK has also flagged another aspect of the movement of a solid body through a fluid, which is worthy of consideration in aircraft design. That aspect is "hull speed".

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possibly the denser water could have a higher drag co efficient and bringg it all back to the same speed.

We could go on finding little differences for ever at this rate.

How about some simpler question OME. I will have to think one up.

How about. I am on finals in my Corby. On the best speed and am falling below my desired glide slope. I respond by pushing the stick forward slightly and surprisingly am back on the correct slope. Why?

Give them a bit of time Nev.

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The actual answer is that whichever ship has the most favourable tides will go faster, this factor being much more important than air density. It also overcomes the issue of hull speed.

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21 hours ago, Yenn said:

possibly the denser water could have a higher drag co efficient and bring it all back to the same speed.

We could go on finding little differences for ever at this rate.

How about some simpler question OME. I will have to think one up.

How about. I am on finals in my Corby. On the best speed and am falling below my desired glide slope. I respond by pushing the stick forward slightly and surprisingly am back on the correct slope. Why?

Give them a bit of time Nev.

I find it best to just land the aircraft..............

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I doubt calculating the inertia change when the wind "HITS" the sail is going to represent the TRUE situation. Nev

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You have confused "inertia" with momentum.

Newton's First Law of Motion provides the definition of "inertia" - A body at rest ..... The amount of inertia a body possesses is solely dependent on its Mass. Mass is the total of the atoms and molecules in the body. Weight is related to mass by being the size of the force a mass can exert when accelerated by the local force of Gravity.

Since Force = Mass x Acceleration, if we put an object on a weighing scale and find that the scale reads 2.35 kilograms, then that is the Force the object is exerting on the scale mechanism. But what is the mass of the object?

Since Force = m.a, and the object at sea level is being subjected to the acceleration due to Gravity (9.81 metres/per second/per second), then

2.35 = m x 9.91

2.35/9.81 = m

m = 0.239 kgs

But for practical purposes, we equate Mass and Weight.

Momentum is the property possessed by an object in motion. Its magnitude is the product of its mass and its velocity.

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Hmmmm, Force is measured in Newtons. The scale in your above example converts the force applied to Kg so you don't have to do the calculation.

If the scale reads 2.35kg the object is actually applying a force of 23.05N to the scale.

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Inertia CHANGE covers it. To change, it has to be accelerated or decelerated.. Nev

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3 hours ago, old man emu said:

You have confused "inertia" with momentum.

Newton's First Law of Motion provides the definition of "inertia" - A body at rest ..... The amount of inertia a body possesses is solely dependent on its Mass. Mass is the total of the atoms and molecules in the body. Weight is related to mass by being the size of the force a mass can exert when accelerated by the local force of Gravity.

Since Force = Mass x Acceleration, if we put an object on a weighing scale and find that the scale reads 2.35 kilograms, then that is the Force the object is exerting on the scale mechanism. But what is the mass of the object?

Since Force = m.a, and the object at sea level is being subjected to the acceleration due to Gravity (9.81 metres/per second/per second), then

2.35 = m x 9.91

2.35/9.81 = m

m = 0.239 kgs

But for practical purposes, we equate Mass and Weight.

Momentum is the property possessed by an object in motion. Its magnitude is the product of its mass and its velocity.

a) Inertia and momentum are the same thing.

b) If something is weighed on a scale and the scale says 2.35, then the mass is 2.35 kg. (Assuming the object is not being accelerated and the scale is accurate and being used on the surface of Earth.)

c) You messed up because force is measured in newtons, not kg.

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21 minutes ago, APenNameAndThatA said:

Inertia and momentum are the same thing.

You messed up because you don't know the meaning of Newton's First and Second Laws. Inertia is a concept. Inertia is simply the tendency of an object to follow a straight line trajectory at a constant speed, unless acted upon by an external force. The tendency of an object to resist changes in its state of motion varies with mass. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion. The sense of the word "inertia" comes from the Latin "iners", which means "lazy"

The Momentum of a body is something that it possesses due to the product of its mass and its velocity. We can measure both these quantities to calculate the momentum the body possesses.

3 hours ago, facthunter said:

Inertia CHANGE covers it. To change, it has to be accelerated or decelerated.

NO. Momentum is the thing that changes due to acceleration (positive or negative). You can only change the inertia of a body by adding or removing mass.

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On 02/12/2020 at 8:06 AM, old man emu said:

I should have simplified the whole bloody thing by not posing the question at all. I pose a serious question and get stupid responses. There are times and places for wit and repartee. One of these is called socialaustralia.com.au.

The point of the question, and, dare I say, the title and location where it exists, indicate that it is something to be contemplated in light of pilots' supposed knowledge of the properties of the atmosphere and the effects those properties have on Man and machine.

What you’re seeing here is the result of our culture. We tend to look more deeply into situations and question them before jumping to conclusions. This is one of the reasons Australian apply CRM so well.

Edited by Roundsounds
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OME is right about inertia. It is directly related to MASS (The amount of STUFF in something)and when normal earth gravity (force) acts on it, the weight equals the MASS of it.

Momentum is MASS x Velocity and is useful in deciding what happens when two or more  bodies collide. (Conservation of linear momentum). Kinetic Energy is energy of motion MV squared. and that's the one that causes damage when you hit something solid. More correctly it's the decelerative force you are subject to that does the damage to you. One has to get these terms exactly right..  Obese persons should reduce their Inertia .to live longer. and keep their planes AU inertia legal.Nev

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