# LSA's have a MTOW of 600 kg. My plane flys badly if that weight is exceeded. Can a "virtual weight" be calculated from deviation from standard atmosphere?

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For, like, taking off when it is 45° C?

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for a start, you can fly over the aircraft maximum takeoff weight. It is there for a reason ! DUH

secondly, there should be graphs in the POH which show you the different calculations for density altitude and from this you can calculate your ground roll for temperatures above standard atmosphere and the climb rate to be expected.

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At a guess from 20C to 40C I'd say nearly double the distance.

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Go back to basic theory and use the density calculated for temp, pressure and humidity. By the time you have done it, it will have changed.

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I hope I've read into the question correctly and we are back into the Lift equation, albeit this time in purely practical terms

We want to calculate what conditions are need for a wing to generate sufficient Lift to balance, or exceed the weight of the aircraft. So let's look at what can and cannot change in that formula.

Total Lift - This is the result of the calculation.

Coefficient of Lift - unchangeable as it is part of the aerofoil design

Density - We know that is a variable thing.

Velocity - That's in True Airspeed, and since density and temperature are involved, it is a variable

Wing Area - That is part of the aircraft design so in unchangeable.

If we acknowledge the involvement of Coefficient of Lift and wing area in lift creation, but know that they are not variables, we can assign them the value of one (1) for calculation purposes.

Therefore the Lift equation becomes

Lift = {1 x (density x TAS)^2 x 1} /2

If you know the air density and the TAS you can calculate Lift. If, on the other hand , you know what Lift you need, then you have to fiddle with density and TAS. In this case, because you are operating from a certain altitude and at a certain known density, then by pluging in the known density and fiddling with the TAS you can calculate how much faster your takeoff speed will be above the speed for MYOW.

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IF your plane just gets to say 5000 feet it  alt  on a normal day, it won't get off the ground with a DA of 5000 feet existing. There are rules of thumb for calculating DA. Nev

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What Facthunter says is true, but I thought that the question started in the simplest situation - seal level in a standard atmosphere. If you do the calculations for that, then you get a table basically of rotation speed and aircraft take off weights. Then you could create tables for those values at different densities.

A thing you have to know is the maximum TAS the aircraft can attain after a ground run, and still clear, say. a 50 ft high object. Obviously, there comes a point where there is insufficient runway length for that.

Here we go with the algebra!

v^2 = u^2 + 2as

where v = final velocity

u = initial velocity

a = acceleration

s = distance

Rearranging the  terms to solve for "s" we get

1/2 (v^2/a) = s

Where can we get a value for "a" from?

We could do a time trial to determine average acceleration and use

a = (v - u)t

where t = elapsed time.

However, since acceleration is

a = F/m

Every time you changed the weight of the aircraft you would have to recalculate the average acceleration since F is coming from the Thrust generated ultimately by the engine, there is a limit to that, which one would have to know.

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all of this should be in the manual for every aircraft. They are easy formulas to calculate but some manufacturers include simple tables like this for people that don't have a calculator

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2 hours ago, FlyBoy1960 said:

They are easy formulas to calculate but some manufacturers include simple tables like this for people that don't have a calculator

That table is not good for answering the OP's original question. If the published MTOW is exceeded, can you calculate how much above it the wings can lift.

Clearly the question relates to going beyond manufacturer's advice. Remember that the in one famous operation in DC-3 (or C-47) aircraft, they overloaded the planes like a Tokyo commuter train and they still flew.

I'm hoping for some discussion on the assumptions I made. This is an interesting topic.

There is one factor that the Lift formula cannot account for, and that is the location of the Centre of Gravity. I suspect that an aircraft's wing is capable of generating very much more lift that would be required, but getting the Balance within the envelope might be the idea's killer.

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if you overload the wing by going past the designed lift profile you will get laminar flow separation.

This is also called laminar bucket and the aircraft will not fly, it will drag its tail around the sky with a high angle of attack and it heavy enough will just sink. Pushing the stick forward does nothing except change the angle of attack slightly but it doesn't produce any more lift.

Simple answer is,  don't fly over the maximum takeoff weight of the aircraft.

I don't know why we are even talking about this because it requires an approval from CASA each and every time you want to do this and it is only approved for things like ferry flights where you are carrying extra fuel coming over from the states ?

I don't really want to sound like Capt obvious that this is such a bad idea. Just don't flly overweight !

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The "P" charts for the DC-3 in PNG were stretched to allow more AUW on the grounds the area was "developmental". (PK) charts. All BS really as the plane just didn't perform. The general limit on ability to climb higher or carry more weight is available POWER from the engines assuming the structure is strong enough.  G of G is a matter of being able to CONTROL it in PITCH. The tail plane CAN carry some of the weight.. The best AoA of the wing will give best efficiency and the speed used must increase to enable that AoA  to remain as you get heavier or higher. As you go faster( INDICATED airspeed) the parasite drag  (Non lift associated drag) will increase as a % . This situation can be improved by increasing wingspan to reduce the airspeed needed.

You don't need extra lift to  climb. You need a bit to commence the climb. . Nev

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I'm not sure what you mean by "flys badly". If it truly flys badly it probably isn't a temperature thing.

There are a number of factors that might influence MTOW:

- Structure - how strong is the airframe?

- Regulations e.g. a limit on MTOW or stall speed

- Performance - the ability to climb after takeoff, or go around in landing configuration

Temperature and altitude (i.e. air density) affect the true airspeed you need to fly and also the power available from the engine i.e. decreasing density has a double effect.

It is possible to translate a high temperature into an equivalent lower temperature at a higher altitude. This is part of the performance subject in the PPL syllabus. It's more likely to be part of runway distance calculations than absolute MTOW though. I guess it is possible to have density limits on MTOW for climb performance, but I can't think of any examples.

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Climb limits are often used. Always used with bigger stuff. Near and distant obstacles must be considered if they exist. Take off distance usually includes to a certain height.. Indicated airspeed allows for density height. Approach climb is a requirement to be met in some circumstances. Certainly  a density height may be  obtained by different combinations of pressure and temperature..  Density or altitude limits do exist as at high ALTITUDE AERODROMES the high groundspeed may exceed  normal tyrespeed limits and  require small flap settings to achieve the required climb rate on lift off.  Also the nosewheel may have to be fitted with brakes to reduce accelerate - stop distances at places like Teheran in IRAN. and Khartoum. Nev

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Am I missing something here: This would appear to be the second time, in just a few weeks, when a Forum member could be thought to be confession/advocating the deliberate breaking of the rules covering the operation of an RAA registered aircraft.

Its bad enough (completely nuts) that such an action is being mentioned, in print,  but then good people (Forum members) start to discuss the merits (there are non) of the  action is mind boggling.

Get real people, this is how the authorities not only investigate/prosecute the "offenders" but may also take action against the Forum that allows such debate to take place.

I am all for free speech, responsibly conducted but am appalled at the risk that would seem to be being taken both by the initiator of this topic and the Forum .

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I second this motion, just stupidity.  Delete the entire thread imo

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Isn't the OP asking what weight would give the same performance at 45°C as he gets at 600kg and 15°C?

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15 minutes ago, Thruster88 said:

Isn't the OP asking what weight would give the same performance at 45°C as he gets at 600kg and 15°C?

Quite possibly, and it is a good question. I wish he'd come back and comment on what has been posted.

Isn't it true that there are some aircraft that in Australia are limited by legislation to a MTOW of something like 600 kg, but under legislation elsewhere are permitted 750 kg? And there are no differences between the Australian aircraft and the European one?

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First up, some LSA aircraft have a MTOW of 540kg, not 600kg. Secondly, as far as I know, LSA aircraft don't have the 'P' charts like I used to use when flying the Piper and Tobago. Maybe I'm wrong, but no P charts with my Jabiru. And thirdly, who would fly in 45°C temperatures? That's front bar temperatures. And, going by memory (that's had a few ports this evening) 45°C would give a density height of over 6000 feet in ISA conditions.

Edited by Jabiru7252
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Apennameandthat has one of these, A-22LS which is the Light-sport version for the American market with a higher gross weight of 600 kg (1,323 lb) for the landplane and 650 kg (1,433 lb) for the seaplane. So, if you add a really drag-inducing undercarriage you can increase the MTOW by 50 kg. It seems logical that the same plane, with a much less drag-inducing u/c can easily take off with  an all-up weight of 650 kg.

Using this data from Camden airport at 4:00pm 22/1/21

Airfield elevation: 230'

Temperature : 36C

Air pressure: 1005.9 mb

Humidity 13%

you get a density altitude of 3100'

11 hours ago, skippydiesel said:

a Forum member could be thought to be confession/advocating the deliberate breaking of the rules covering the operation of an RAA registered aircraft.

If you take note of the title to this thread, it contains the word "VIRTUAL". To me that implies that the question calls for an exploration of the effects of putting a variety of numbers into the Lift formula,

Lift = {1 x (density x TAS)^2 x 1} /2

turning the handle and seeing what comes out the other end. There's no inference that anyone has, or plans to, use the results of that exploration to exceed the MTOW of their aircraft. If anything, the results of the exploration would show that

1. Lift is dependant on air density for a given TAS

2. Lift is dependant on TAS for a given air density

3. Lift is dependant on the combined effects of air density and TAS.

For those who don't like working with algebra and mathematics, the exploration would show that for a given air density different from 1013 mb you have to go faster to get the same lift as at 1013 mb. This translates to:

1. Faster speed on the ground before you can rotate, and the other way, faster speed on the ground at the flare.

2. Longer ground roll on take off because it takes longer to accelerate to rotation speed, and the other way because touchdown ground speed is higher.

3. Longer ground roll on take off because air density affects power output of normally aspirated IC engines.

I'm not going to list the further effects of temperature and density on aircraft performance once in the air as that's worth its own thread.

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28 minutes ago, old man emu said:

you have to go faster to get the same lift as at 1013 mb

Also the engine power is reduced (unless you have a turbo) so acceleration is reduced which increases the time it takes to get to the higher speed.

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53 minutes ago, aro said:

Also the engine power is reduced (unless you have a turbo) so acceleration is reduced which increases the time it takes to get to the higher speed.

I said I wasn't going to talk about that in this thread. Not that the statement is incorrect, though.

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Everything suffers as you get less dense air . The prop, engine,  lift, you etc drag also reduces. Indicated airspeed is still OK for stall indication/margins. Some flutter occurrences relate to true airspeed so be wary at higher altitudes. Nev

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4 hours ago, facthunter said:

Everything suffers as you get less dense air .

That's so true!

We all know that hot air is less dense than cold air. They have a specially constructed Chamber in Canberra where hot air accumulates. As a result, we all suffer.

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The concentration of politicians in Canberra can be quite Dense.. They spare no effort in this regard. Nev

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22 hours ago, Jabiru7252 said:

First up, some LSA aircraft have a MTOW of 540kg, not 600kg. Secondly, as far as I know, LSA aircraft don't have the 'P' charts like I used to use when flying the Piper and Tobago. Maybe I'm wrong, but no P charts with my Jabiru. And thirdly, who would fly in 45°C temperatures? That's front bar temperatures. And, going by memory (that's had a few ports this evening) 45°C would give a density height of over 6000 feet in ISA conditions.

Some manufacturers have placed a maximum temperature operating limit on their aircraft for reasons of structural strength but mostly for limiting their liability when a pilot tries to fly in clearly unsuitable conditions.  I think Jabs are restricted to 39o?

The older P charts for GA aircraft had a number of small graphs which brought into play many features in the takeoff, including altitude temperature, strip length, strip slope, strip surface, and wind. At the end of the tortuous following the current numbers for each - one arrived at a MTOW for that situation.  Then, and here's the kicker - there was a 'reverse' line on the graph which then determined whether your aircraft, loaded at that weight, and under those conditions, could actually meet a climb gradient of 6 degrees? I think.  It is often the case that you can takeoff from an airport, usually with a huge down slope, but your aircraft cannot meet a climb requirement, and you spend the next few exciting minutes going below the level of the strip from which you've just taken off. It often ended badly.

Having survived quite a few hours flying commercially in high and hot conditions, I'm not about to advise anyone untrained in handling them, to start overloading their considerably lower HP RAAus aircraft .  Don't do it!  Have a personal limit on conditions as well as all the other stuff.  Fly early in the day.