Relation between lift force of airfoils and speed + airfoils and thrust vs atmosphere density

[Pinneman]

Hi everyone!

Does any of you know how speed affects lift force?

If 2 wings S give 130 000 Newtons this value is given for what speed?

Also how this force changes with atmosphere density? If this linear, 50% atmosphere is 50% lift force or there is a square root? Same for thrust of atmosphere engines.

 

Thank you!
See you in space.

Pinne

[Haunty]

I don't know if the math formulas have been made public. I've seen people do data gathering with Lua to find that stuff out, but I don't remember where that info is now.

[Leonim]

On 10/13/2022 at 5:38 PM, Pinneman said:

Does any of you know how speed affects lift force?

If 2 wings S give 130 000 Newtons this value is given for what speed?

Also how this force changes with atmosphere density? If this linear, 50% atmosphere is 50% lift force or there is a square root? Same for thrust of atmosphere engines.

 

Max Lift is possible as soon as you pass the sustentation limit for your construct's weight, depending on the current gravity and thus altitude (for an estimation, in build mode, check the building helper / atmospheric flight engineer / high altitude lift).

To simplify, you can potentially reach max lift as soon as you have at least 1g of thrust.

 

Anyway, the default in-game Flight System only use that potential lift to counter the gravity force and air friction for your given throttle (or cruise speed), unless you hit the spacebar for full lift using all the construct's vertical capabilities. If for one reason or another (too much angle, loss of power, less atmosphere, higher cross-section) you don't have enough lift, you fall, simple as that.

 

If I remember correctly, during early Beta, the Lift Power in kN (kilo-Newtons) was the required power to fly 1t (ton) at 125m/s on Alioth (with a gravity around 9.8, not taking air resistance into account).

 

Since I have some downtime, you're in for a long post, quite a rarity for me nowadays.

 

---

Yet with simplified aerodynamics, your Current Lift mainly depends on your Angle of Attack (the ship's orientation compared to the "horizontal" plane: generally pitch is what matters if you are level, plus roll and yaw as well when not properly aligned). Ailerons, Stabilizers and Wings have different preferences before they reach their specific stall angles, which are way higher than in our non-futuristic real world, but may still be a worry.

 

Note that your current lift is not that much affected by the ship orientation but you must stay aware of the basics: "root(cos(AoA))" act as a multiplier. For instance an AoA of 20° "only" provides 97% of your lift, while its reduced to 84% for 45° but then you are close to Stalling anyway (and already have with ailerons). Beware that pitching, rolling and turning at the same time causes cumulative dampening of your lift power... and sooner stalls.

 

To avoid further stalling, and a potential Death spiral dreaded by any pilot, the easiest way in-game is to align your ship back with your current velocity's vector to regain control (use the X shortcut to visualize that trajectory)... as long as you have enough altitude for that maneuver.

 

Since every construct is built differently with a mix of Airfoils, the AoA to achieve Max Lift may vary, but less than in real-life since all in-game forces are applied from/to the construct's center of mass (visible in the builder helper) and the angles are so far the same within an airfoil category. If you are mainly using wings, you are fine up to a whooping angle of 50°. Ailerons have closer specs to IRL wings, which means they stall earlier, above 30°, but help with fine adjusting the torque (by +/- 5°). Finally, stabilizers were not meant to be used as horizontal airfoils, but don't stall until 70°.

 

As a guideline for ascending the fastest, aim for half those values for the Sweet Spot between improving the sustentation power and reducing the lift-induced drag (air friction). You can check the wikipedia article on "Lift-to-drag ratio" ratio for more information and the why. Too much angle and you'll lose too much speed due to air friction, even if your airfoils are not yet stalled.

 

For the sake of information, the Lift/Drag ratio (shown in item inspection) should tell you how aerodynamic is an airfoil. It also hints about which angle would be best suited to land horizontally with, mainly irrevelant since we use omni-directional brakes and hovers (and/or vertical boosters) to achieve vertical landings and takeoffs (VTOL).

 

What affects your overall atmospheric speed the most are Cross-section Surfaces: the frontal one define the construct's current air resistance/friction (the drag, which is the other force going against your atmospheric flight), the horizontal ones is supposed to help you with lift, and the vertical one against drift.

 

Again simplified maths, since as far as I know, the only time when the "real" cross-section (facing your current trajectory) is used is for damage checks during Atmospheric Reentry, so aim wisely: like you would dive in water. Otherwise, the frontal cross-section is used to compute air friction, and thus is one of the main concerns (with mass and its distribution a.k.a. inertia matrix) for ship designers like myself, aiming for efficient and fast constructs.

 

Indeed it means that in space, nobody can hear you crying about the bulking shapes of some constructs, since cross-sections don't matter there. 😛

 

---

Did you know? Atmospheric engines only provide half their power on the vertical axis to begin with, so yes if you provide 1g of vertical thrust with those, your sustentation speed is effectively 0... while they are fueled.

 

At the time of writing I do not know the specifics of how atmospheric density impacts the power of atmospheric engines: they obviously stop at 0%, and min out when you reach high altitude. With a density under 10%, you will need approximatively 1.6 lift more than at sea level, but then the space engines can gradually kick in and help you leave the atmosphere or continue onwards a Suborbital Flight path (which is the most fuel-effective imo).

 

If someone has the formula for calculating the atmospheric density at any given altitude from planet informations like atmosphere thickness and radius, thanks for sharing.

 

[Pinneman]

Hi Leonim!

I though this topic will just die out therefore I am so happy to see your input.
I am totally new in this game but not is physics whatsoever. Although aeronautics is not my domain I checked if the developers did not adopt some of the well known physics. Well, it turned out they did and I am happy to share my findings. 

 

So far I did a calculations for wing size m and if aircraft have only these than sustentation speed can be calculated as of function of:

- percent of atmosphere [%]

- aircraft weight [t]

- amount of wings []

- gravity [g]
 

The equation goes:

Sustentation speed [m/s] = SQRT(((gravity * aircraft_weight * 1000) / amount_of_wing_m) / (percent_of_atmosphere * 50,1))

 

Therefore if:

- Ship weight is 140 tons,

- Gravity is 9,8 m/s

- Atmosphere density 100% 

- 4 wings M

Sustentation speed is - 82,83 m/s

Accuracy is circa +/- 2%

 

Therefore at 10% atmosphere and 0,9g gravity sustentation speed for the same ship is 248,48 m/s. That also answer the question - "what should be my max speed to get off a planet" in the way that "your max speed should be above 248,48 m/s to leave the planet". If you load 40 tons of cargo it becomes 281,75 m/s. Pretty handy equation. I will develop it for more wing types.

 

Speaking of engines. Engine_thrust(atmosphere_density) function is linear. They also use air resistance which is also linear to atmo density. This is how they keep max speed regardless of altitude. You can notice it by travelling at high attitude - you will experience same speed but your fuel will last for many  times longer. In other words - with 50% atmo density you will consume twice as much fuel with the same speed than at 25% atmo density. So as long as you fly horizontally all is good. I see 10% error but I am 95% sure relation is linear. That may be due to low amount of data,

 

Once you want to increase the altitude at high altitude a ship begins to behave totally different than in low altitudes. At 10% of atmo thrust is just 10% and wings are key lift force here. At low altitude, with thrust 2 g you can start easily and high rising angles don't kick back (engine is strong enough so if your lift drops due to high angle you are still good as engine is stronger than gravity) but at 10% atmo the thrust goes from 2 g to 0,2 g so high angles make you fall easily even with small angles. From what you wrote I guess you are pretty comfortable with vectors and trigonometry so I will skip the explanation. Keeping a high speed and low angles is therefore essential at high altitudes. As in the equation above, at 10% atmo sustentation speed of 140 tons ship with 40 tons of cargo is 281,75 m/s. Lower max speed will not allow you to reach the space engine activation altitude. Also if your speed during ascending will drop below 281,75 m/s (at 10% atmo) you will see your ship falling. It is also how my equation and max speed shown in construct can answer the question - "will I reach space?"

 

On top of that I found out that these guys are geeks. I love it! It must be fun to work there.

 

P.S.
In real life air resistant is proportional to 3rd power of speed. So increasing speed by 10% will increase the resistance by 33.1% I assumed such a relation at a beginning and it took me w while to figure out why things are not adding up. Assumption that fuel consumption is linear to thrust actually helped me to solve it. It is still an assumption though.

Edited October 18, 2022 by Pinneman

[GraXXoR]

On 10/18/2022 at 7:00 PM, Leonim said:

 

Did you know? Atmospheric engines only provide half their power on the vertical axis to begin with, so yes if you provide 1g of vertical thrust with those, your sustentation speed is effectively 0... while they are fueled.

 

 

 

Are you saying that a 100kN engine will only provide 50kN of power in a vertical orientation?

[Pinneman]

I made a fast test and took ship with these parameters

1. Weight 3 760 kg
2. Thrust 80 000 N thrust

I flight with a speed vector parallel to gravity. I repeated this procedure couple of times to find the height (atmosphere density) where my ships stops as gravity is equal to engine thrust.

I found out that it happened at circa 46% atmosphere density. Therefore at 46% atmosphere density and 0,9g at that level, the initially 80 kN engines get thrust = 3 760 kg * 0,9 * 9,82 m/s^2 = 33,2 kN. It means engines had just 41,5% of power. This is consistent with atmosphere density which was 46% and my finding from previous post. Please note that there was inertia involved and it was difficult to stabilize vectors parallel. Considering this the result seems precise enough.

 

Important note!
Engine was not mounted on vertical axis but the direction of flight was vertical. Theoretically it should not matter and in a real life it does not but it is still possible that developers, for some reason, implemented it that way. I will need to verify in another test.

Edited October 20, 2022 by Pinneman

[GraXXoR]

6 hours ago, Pinneman said:

I made a fast test and took ship with these parameters

1. Weight 3 760 kg
2. Thrust 80 000 N thrust

I flight with a speed vector parallel to gravity. I repeated this procedure couple of times to find the height (atmosphere density) where my ships stops as gravity is equal to engine thrust.

I found out that it happened at circa 46% atmosphere density. Therefore at 46% atmosphere density and 0,9g at that level, the initially 80 kN engines get thrust = 3 760 kg * 0,9 * 9,82 m/s^2 = 33,2 kN. It means engines had just 41,5% of power. This is consistent with atmosphere density which was 46% and my finding from previous post. Please note that there was inertia involved and it was difficult to stabilize vectors parallel. Considering this the result seems precise enough.

 

Important note!
Engine was not mounted on vertical axis but the direction of flight was vertical. Theoretically it should not matter and in a real life it does not but it is still possible that developers, for some reason, implemented it that way. I will need to verify in another test.

 

Rounding numbers because I'm in a bar... but...

 

 a ship with 8000Kg thrust balances an almost 4000kg load at almost 50% atmosphere.

seems about right using the DU model.

[Leonim]

On 10/19/2022 at 2:05 PM, Jinxed said:

 

Are you saying that a 100kN engine will only provide 50kN of power in a vertical orientation?

 

Not exactly, a 100kN engine would indeed provide its full thrust power in vertical orientation, but it will only translate to 50kN in lift power. I should have been more accurate in my phrasing.

 

It can be checked with the Builder Helper (section "Atmospheric Flight Engineer": Max Thrust, Low and High Altitude Lift), and experienced with a simple build. Note that using a gyroscope to change the orientation of the contruct is modifying this behaviour coherently.

 

Still, atmospheric engines to my experience (at least with no more than basic pilot skills) still provide half their power as lift (along the gravity vector).

 

---

Thank you Pinneman for doing that test, but it can still be interpreted as your engines using 83% of their power (80kN) to provide those 33,2kN of lift.

 

To my comprehension, if your ship mass would have been above 4 600kg, your ship would not have been able to stay stationary and would slowly descend. With a mass of lets say 6t, that setup (vertical atmospheric engines) should not be able to even lift above what your ground engines have as height range, no matter the orientation, only wasting fuel in the futile process (and quite a lot at that, since trying at full power).

 

---

Sadly, the default autoconf controls don't use subtags priorities to enforce the use of "ground"-tagged engines before adding the "not-ground" ones to the mix. Since the job is distributed evenly to all lift-capable engines, hovering cost way more fuel than it should if your setup has some vertical engines. Just a reminder but hover engines are way more fuel-effective than atmo engines, by at least a factor of 50 for the worse of them, so better tweak those controllers in such cases.

 

On a side note, the Hornet in the Air Challenge mission can be effectively used for the final deliver on the flying fortress after using the Freelancer (linked container) to hover and gather everything below, but with neither a gyro's axis swap nor auto-level features, it is still safe but unwieldly to lift/land vertically (easier to brake/crash landing in a hurry, yet nice training for vertical maneuvers).

 

Back on track, somewhat, an "Hover Engine S" can provide 50kN of max lift, same as the least powerful airfoil, the "Compact Aileron XS": atmospheric constructs are indeed meant to fly like planes. Though if you want to be fuel effective, thanks to adjustors, they can copter at very low altitudes (using only hover engines to move around). And even glide (only airfoils) if you build them right, though without aerial currents, its quite the challenge to regain potential energy, still very useful for feather landings.