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Signed-off-by: Ramon Roche <mrpollo@gmail.com>
Co-authored-by: Ramon Roche <mrpollo@gmail.com>
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docs/ko/config_fw/index.md
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# Fixed-wing Vehicle Configuration
Fixed-wing configuration and calibration follows the same high level steps as other frames: selection of firmware, configuration of the frame including actuator/motor geometry and output mappings, sensor configuration and calibration, configuration of safety and other features, and finally tuning.
:::info
This topic is the recommended entry point when performing first-time configuration and calibration of a new multicopter frame.
:::
The main steps are:
- [Standard Configuration](../config/index.md)
- [Autotune](../config/autotune_fw.md) - PID Tuning
::: info
Autotune simplifies the manual process described in: [Fixed-wing Rate/Attitude Controller Tuning Guide](../config_fw/pid_tuning_guide_fixedwing.md).
:::
- [Fixed-wing Altitude/Position Controller Tuning Guide](../config_fw/position_tuning_guide_fixedwing.md)
- [Fixed-wing Trimming Guide](../config_fw/trimming_guide_fixedwing.md)
docs/ko/config_fw/pid_tuning_guide_fixedwing.md
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# Fixed-wing Rate/Attitude Controller Tuning Guide
This guide explains how to manually tune the fixed-wing PID loop.
It is intended for advanced users / experts, as incorrect PID tuning may crash your aircraft.
:::info
[Autotune](../config/autotune_fw.md) is recommended for most users, as it is far faster, easier and provides good tuning for most frames.
예를 들어, 새로운 ESC 또는 모터에는 다른 튜닝 게인이 필요합니다.
:::
## 전제 조건
- Trims must be configured first (before PID turning).
The [Fixed-Wing Trimming Guide](../config_fw/trimming_guide_fixedwing.md) explains how.
- Incorrectly set gains during tuning can make attitude control unstable.
A pilot tuning gains should therefore be able to fly and land the plane in [manual](../flight_modes_fw/manual.md) (override) control.
- Excessive gains (and rapid servo motion) can violate the maximum forces of your airframe - increase gains carefully.
- Roll and pitch tuning follow the same sequence.
The only difference is that pitch is more sensitive to trim offsets, so [trimming](../config_fw/trimming_guide_fixedwing.md) has to be done carefully and integrator gains need more attention to compensate this.
## Establishing the Airframe Baseline
If a pilot capable of manual flight is available, its best to establish a few core system properties on a manual trial.
To do this, fly these maneuvers.
Even if you can't note all the quantities immediately on paper, the log file will be very useful for later tuning.
:::info
All these quantities will be automatically logged.
You only need to take notes if you want to directly move on to tuning without looking at the log files.
- 편리한 속도로 수평 비행하십시오.
스로틀 스틱 위치와 대기 속도를 기록하십시오 (예 : 70 % → 0.7 스로틀, 15m/s 대기 속도).
- 최대 스로틀과 10-30 초 동안 충분한 대기 속도로 상승하십시오 (예 : 12m/s 대기 속도, 30초에 100m 상승).
- 스로틀이 0이고 적절한 대기 속도로 10-30초 동안 하강합니다 (예 : 18m/s 대기 속도, 30초에 80m 하강).
- 60도 롤이 될 때까지 전체 롤 스틱을 사용하여 오른쪽으로 강하게 쌓은 다음 반대쪽에서 60도까지 전체 롤 스틱으로 왼쪽으로 강하게 저장합니다.
- 45도를 높이고 45도를 낮춥니다.
:::
This guide will use these quantities to set some of the controller gains later on.
## Tune Roll
Tune first the roll axis, then pitch.
The roll axis is safer as an incorrect tuning leads only to motion, but not a loss of altitude.
### 피드포워드 게인 조정
To tune this gain, first set the other gains to their minimum values (nominally 0.005, but check the parameter documentation).
#### Gains to set to minimum values
- [FW_RR_I](../advanced_config/parameter_reference.md#FW_RR_I)
- [FW_RR_P](../advanced_config/parameter_reference.md#FW_RR_P)
#### 튜닝 대상 게인
- [FW_RR_FF](../advanced_config/parameter_reference.md#FW_RR_FF) - start with a value of 0.4.
Increase this value (doubling each time) until the plane rolls satisfactorily and reaches the setpoint.
프로세스가 끝나면 게인을 20% 낮춥니 다.
### 속도 게인 조정
- [FW_RR_P](../advanced_config/parameter_reference.md#FW_RR_P) - start with a value of 0.06.
시스템이 흔들리거나 트위치를 시작할 때까지 이 값을 늘립니다 (매번 두 배로 증가).
그런 다음 게인을 50% 줄입니다.
### 적분기 게인으로 트림 오프셋 조정
- [FW_RR_I](../advanced_config/parameter_reference.md#FW_RR_I) - start with a value of 0.01.
명령된 롤 값과 실제 롤 값 사이에 오프셋이 없을 때까지이 값을 늘립니다 (매번 두 배로 증가) (로그 파일을 확인해야 할 가능성이 높음).
## Tune Pitch
The pitch axis might need more integrator gain and a correctly set pitch offset.
### 피드포워드 게인 조정
To tune this gain, set the other gains to their minimum values.
#### Gains to set to minimum values
- [FW_PR_I](../advanced_config/parameter_reference.md#FW_PR_I)
- [FW_PR_P](../advanced_config/parameter_reference.md#FW_PR_I)
#### 튜닝 대상 게인
- [FW_PR_FF](../advanced_config/parameter_reference.md#FW_PR_FF) - start with a value of 0.4.
Increase this value (doubling each time) until the plane pitches satisfactory and reaches the setpoint.
프로세스가 끝나면 게인을 20% 낮춥니 다.
### 속도 게인 조정
- [FW_PR_P](../advanced_config/parameter_reference.md#FW_PR_P) - start with a value of 0.04.
시스템이 흔들리거나 트위치를 시작할 때까지 이 값을 늘립니다 (매번 두 배로 증가).
그런 다음 게인을 50% 줄입니다.
### 적분기 게인으로 트림 오프셋 조정
- [FW_PR_I](../advanced_config/parameter_reference.md#FW_PR_I) - start with a value of 0.01.
명령된 피치 값과 실제 피치 값 사이에 오프셋이 없을 때까지이 값을 늘립니다 (매번 두 배로 증가) (로그 파일을 확인해야 할 가능성이 높음).
## Adjusting the Time Constant of the Outer Loop
The overall softness / hardness of the control loop can be adjusted by the time constant.
The default of 0.5 seconds should be fine for normal fixed-wing setups and usually does not require adjustment.
- [FW_P_TC](../advanced_config/parameter_reference.md#FW_P_TC) - set to a default of 0.5 seconds, increase to make the Pitch response softer, decrease to make the response harder.
- [FW_R_TC](../advanced_config/parameter_reference.md#FW_R_TC) - set to a default of 0.5 seconds, increase to make the Roll response softer, decrease to make the response harder.
## Other Tuning Parameters
이 가이드에서는 중요한 매개변수들을 설명합니다.
Additional tuning parameters are documented in the [Parameter Reference](../advanced_config/parameter_reference.md).
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# Fixed-wing Altitude/Position Controller Tuning
이 가이드는 비행 임무와 고도 및 위치 제어 모드에서 고정익 컨트롤러를 정밀 조정에 많은 도움이 됩니다.
PX4 uses TECS for altitude and airspeed control, and NPFG for horizontal heading/position control.
:::info
An incorrectly set gain during tuning can make altitude or heading control unstable.
따라서 TECS 게인 조정시에는 안정된 제어 모드에서 비행기를 비행하고 착륙시킬 수 있어야합니다.
:::
:::tip
All parameters are documented in the [Parameter Reference](../advanced_config/parameter_reference.md#fw-tecs).
이 가이드에서는 중요한 매개변수들을 설명합니다.
:::
## TECS 튜닝 (고도 및 대기 속도)
TECS (Total Energy Control System)는 항공기의 고도 및 대기 속도를 제어하기 위해 스로틀과 피치 각도 설정점을 조정하는 고정익 가이드 알고리즘입니다.
For a detailed description of the TECS algorithm and the control diagram, see [Controller Diagrams](../flight_stack/controller_diagrams.md).
A well-tuned attitude controller is required before tuning TECS: [PID Tuning Guide](../config_fw/pid_tuning_guide_fixedwing.md).
TECS 튜닝은 주로 기체 제한을 올바르게 설정하는 것입니다.
이러한 제한은 아래에 설명된 일련의 비행 기동으로부터 결정될 수있는 매개변수로 설정할 수 있습니다.
Most of the maneuvers required the plane to be flown by a pilot in [Stabilized flight mode](../flight_modes_fw/stabilized.md).
:::tip
It is highly beneficial to have a person available who can read and take note of telemetry data while the pilot is flying the maneuvers.
정확성을 높이기 위해 비행 중에 얻은 데이터를 비행 로그에 기록된 데이터로 확인하는 것이 좋습니다.
:::
#### 1 차 : 트림 조건
Fly in [stabilized mode](../flight_modes_fw/stabilized.md) and find trim values for both throttle and pitch angle for level flight at trim airspeed.
스로틀로 속도와 피치를 조정하여 수평 비행을 유지하십시오.
다음 매개 변수를 설정하십시오.
- [FW_AIRSPD_TRIM](../advanced_config/parameter_reference.md#FW_AIRSPD_TRIM) - set to the desired trim airspeed flown during the maneuver.
- [FW_THR_TRIM](../advanced_config/parameter_reference.md#FW_THR_TRIM) - set to the throttle required to fly at trim airspeed.
- [FW_PSP_OFF](../advanced_config/parameter_reference.md#FW_PSP_OFF) - set to the pitch angle required to maintain level flight.
#### 2nd: Airspeed & Throttle Limits
Fly in [stabilized mode](../flight_modes_fw/stabilized.md) and increase throttle while maintaining level flight using pitch control - until the vehicle reaches
the maximum allowed airspeed.
다음 매개 변수를 설정하십시오.
- [FW_THR_MAX](../advanced_config/parameter_reference.md#FW_THR_MAX) - set to the throttle you applied to reach maximum airspeed during level flight.
- [FW_THR_MIN](../advanced_config/parameter_reference.md#FW_THR_MIN) - set to the minimum throttle the plane should fly at.
- [FW_AIRSPD_MAX](../advanced_config/parameter_reference.md#FW_AIRSPD_MAX) - set to the maximum airspeed you achieved during level flight at `FW_THR_MAX`.
#### 3rd: Pitch & Climb Rate Limits
:::warning
Do not use [FW_T_CLMB_MAX](../advanced_config/parameter_reference.md#FW_T_CLMB_MAX), [FW_T_SINK_MAX](../advanced_config/parameter_reference.md#FW_T_SINK_MAX) or [FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN) to specify the desired climb or sink performance you would like to get from the vehicle!
The parameters define the operating limitations and they should be set during the tuning phase, as described below.
:::
Fly in stabilized mode, apply full throttle (`FW_THR_MAX`) and slowly increase the pitch angle of the vehicle until the airspeed reaches `FW_AIRSPD_TRIM`.
- [FW_P_LIM_MAX](../advanced_config/parameter_reference.md#FW_P_LIM_MAX) - set to the pitch angle required to climb at trim airspeed when applying `FW_THR_MAX`.
- [FW_T_CLMB_MAX](../advanced_config/parameter_reference.md#FW_T_CLMB_MAX) - set to the climb rate achieved during the climb at `FW_AIRSPD_TRIM`.
Fly in stabilized mode, reduce the throttle to `FW_THR_MIN` and slowly decrease the pitch angle until the vehicle reaches `FW_AIRSPD_MAX`.
- [FW_P_LIM_MIN](../advanced_config/parameter_reference.md#FW_P_LIM_MIN) - set to the pitch angle required to reach `FW_AIRSPD_MAX` at `FW_THR_MIN`.
- [FW_T_SINK_MAX](../advanced_config/parameter_reference.md#FW_T_SINK_MAX) - set to the sink rate achieved during the descent.
Fly in stabilized mode, reduce throttle to `FW_THR_MIN` and adjust the pitch angle such that the plane maintains `FW_AIRSPD_TRIM`.
- [FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN) - set to the sink rate achieved while maintaining `FW_AIRSPD_TRIM`.
Specify the target climb and sink rate for autonomous missions by adjusting [FW_T_CLMB_R_SP](../advanced_config/parameter_reference.md#FW_T_CLMB_R_SP) and [FW_T_SINK_R_SP](../advanced_config/parameter_reference.md#FW_T_SINK_R_SP).
These specify the height rates at which the vehicle will climb or descend in order to change altitude.
Furthermore, these two values define the height rate limits commanded by the user in [Altitude mode](../flight_modes_fw/altitude.md) and [Position mode](../flight_modes_fw/position.md).
### FW Path Control Tuning (Position)
All path control parameters are described [here](../advanced_config/parameter_reference.md#fw-path-control).
- [NPFG_PERIOD](../advanced_config/parameter_reference.md#NPFG_PERIOD) - This is the previously called L1 distance and defines the tracking point ahead of the aircraft it's following.
A value of 10-20 meters works for most aircraft.
진동없이 반응이 날카로울 때까지 튜닝하는 동안 천천히 줄입니다.
Vehicles with a slow roll dynamic should have this value increased.
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# 고정익 트리밍 가이드
트림은 트림 조건 (상대적 속도, 공기 밀도, 공격 각도, 항공기 구성 등)에서 제어 표면을 보정합니다.
트림 조건에서 적절하게 트림된 항공기는 조종사 또는 안정화 컴퓨터의 제어 입력 없이도 안정된 자세를 유지할 수 있습니다.
General aviation, commercial and large unmanned planes trim their control surfaces using [trim tabs](https://en.wikipedia.org/wiki/Trim_tab) while small UAVs simply add an offset to the actuator of the control surface.
The [Basic trimming](#basic-trimming) section explains the purpose of each trim parameter and how to find the correct value.
The [Advanced Trimming](#advanced-trimming) section introduces parameters that can be set to automatically adjust the trims based on the measured airspeed and flap position.
## 기본 트리밍
고정익을 적절히 트림하기 위해 사용할 수있는 매개변수가 있습니다.
트리밍 매개변수의 사용 사례에 대한 개요는 다음과 같습니다.
- [RCx_TRIM](../advanced_config/parameter_reference.md#RC1_TRIM) applies trim to the signal received from the RC transmitter.
These parameters are set automatically during [RC calibration](../config/radio.md).
- [CA_SV_CSx_TRIM](../advanced_config/parameter_reference.md#CA_SV_CS0_TRIM) applies trim to a control surfaces channel.
이들은 비행 전에 제어 표면을 기본 각도로 미세하게 정렬하는 데 사용됩니다.
- [FW_PSP_OFF](../advanced_config/parameter_reference.md#FW_PSP_OFF) applies an offset to the pitch setpoint.
항공기가 순항 속도로 비행해야하는 공격 각도를 설정하는 데 사용됩니다.
- [FW_AIRSPD_TRIM](../advanced_config/parameter_reference.md#FW_AIRSPD_TRIM) is used by the rate controllers to scale their output depending on the measured airspeed.
See [Airspeed Scaling](../flight_stack/controller_diagrams.md#airspeed-scaling) for more details.
- [TRIM_ROLL](../advanced_config/parameter_reference.md#TRIM_ROLL), [TRIM_PITCH](../advanced_config/parameter_reference.md#TRIM_PITCH) and [TRIM_YAW](../advanced_config/parameter_reference.md#TRIM_YAW) apply trim to the control signals _before_ mixing.
For example, if you have two servos for the elevator, `TRIM_PITCH` applies trim to both of them.
조종면이 정렬되어 있지만 수동 (안정화되지 않은) 비행 중에 기체가 피치/롤/요잉 업/다운/왼쪽/오른쪽 또는 안정된 비행 중에 제어 신호에 일정한 오프셋이 있는 경우에 사용됩니다.
위의 매개 변수를 설정하는 올바른 순서는 다음과 같습니다.
1. Trim the servos by physically adjusting the linkages lengths if possible and fine tune by trimming the PWM channels (use `PWM_MAIN/AUX_TRIMx`) on the bench to properly set the control surfaces to their theoretical position.
2. Fly in stabilized mode at cruise speed and set the pitch setpoint offset (`FW_PSP_OFF`) to desired angle of attack.
순항 속도에서 필요한 공격 각도는 날개 높이 비행 중에 일정한 고도를 유지하기 위해 비행기가 비행해야 하는 피치 각도에 해당합니다.
If you are using an airspeed sensor, also set the correct cruise airspeed (`FW_AIRSPD_TRIM`).
3. Look at the actuator controls in the log file (upload it to [Flight Review](https://logs.px4.io) and check the _Actuator Controls_ plot for example) and set the pitch trim (`TRIM_PITCH`).
이 값을 수평 비행 중의 피치 신호의 평균 오프셋으로 설정합니다.
로그 조회가 필요가 없거나 수동 모드에서 편안하게 비행 할 수있는 경우 2 단계 전에 3 단계를 수행할 수 있습니다.
You can then trim your remote (with the trim switches) and report the values to `TRIM_PITCH` (and remove the trims from your transmitter) or update `TRIM_PITCH` directly during flight via telemetry and QGC.
## 고급 트리밍
비대칭 익형에 의해 유도된 하향 피치 모멘트는 대기 속도에 따라 증가하고 플랩이 전개 될 때 현재 측정된 대기 속도와 플랩 위치에 따라 항공기를 다시 트리밍하여야 합니다.
For this purpose, a bilinear curve function of airspeed and a pitch trim increment function of the flaps state (see figure below) can be defined using the following parameters:
- [FW_DTRIM\_\[R/P/Y\]\_\[VMIN/VMAX\]](../advanced_config/parameter_reference.md#FW_DTRIM_R_VMIN) are the roll/pitch/yaw trim value added to `TRIM_ROLL/PITCH/YAW` at min/max airspeed (defined by [FW_AIRSPD_MIN](../advanced_config/parameter_reference.md#FW_AIRSPD_MIN) and [FW_AIRSPD_MAX](../advanced_config/parameter_reference.md#FW_AIRSPD_MAX)).
- [CA_SV_CSx_FLAP](../advanced_config/parameter_reference.md#CA_SV_CS0_FLAP) and [CA_SV_CSx_SPOIL](../advanced_config/parameter_reference.md#CA_SV_CS0_SPOIL) are the trimming values that are applied to these control surfaces if the flaps or the spoilers are fully deployed, respectively.
![Dtrim Curve](../../assets/config/fw/fixedwing_dtrim.png)
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A perfectly symmetrical airframe would only require pitch trim increments, but since a real airframe is never perfectly symmetrical, roll and yaw trims increments are also sometimes required.
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# Advanced TECS Tuning (Weight and Altitude)
This topic shows how you can compensate for changes to the [weight of the vehicle](#vehicle-weight-compensation) and the [air density](#air-density-compensation), along with information about the [algorithms](#weight-and-density-compensation-algorithms) that are used.
:::warning
This topic requires that you have already performed [basic TECS tuning](../config_fw/position_tuning_guide_fixedwing.md#tecs-tuning-altitude-and-airspeed).
:::
[Basic TECS tuning](../config_fw/position_tuning_guide_fixedwing.md#tecs-tuning-altitude-and-airspeed) established the key performance limitations of the vehicle that are required for the altitude and airspeed controller to function properly.
While those limitations are specified using constant parameters, in reality vehicle performance is not constant and is affected by various factors.
If changes in weight and air density are not taken into account, altitude and airspeed tracking will likely deteriorate in the case where the configuration (air density and weight) deviate significantly from the configuration at which the vehicle was tuned.
## Vehicle Weight Compensation
Set (both) the following parameters to scale the maximum climb rate, minimum sink rate, and adjust airspeed limits for weight:
- [WEIGHT_BASE](../advanced_config/parameter_reference.md#WEIGHT_BASE) — the weight of the vehicle at which the [Basic TECS tuning](../config_fw/position_tuning_guide_fixedwing.md#tecs-tuning-altitude-and-airspeed) was performed.
- [WEIGHT_GROSS](../advanced_config/parameter_reference.md#WEIGHT_BASE) — the actual weight of the vehicle at any given time, for example when using a larger battery, or with a payload that was not present during tuning.
You can determine the values by measuring the weight of the vehicle using a scale in the tuning configuration and when flying with a payload.
Scaling is performed when _both_ `WEIGHT_BASE` and `WEIGHT_GROSS` are greater than `0`, and will have no effect if the values are the same.
See the [algorithms](#weight-and-density-compensation-algorithms) section below for more information.
## Air Density Compensation
### Specify a Service Ceiling
In PX4 the service ceiling [FW_SERVICE_CEIL](../advanced_config/parameter_reference.md#FW_SERVICE_CEIL) specifies the altitude in standard atmospheric conditions at which the vehicle is still able to achieve a maximum climb rate of 0.5 m/s at maximum throttle and weight equal to [WEIGHT_BASE](../advanced_config/parameter_reference.md#WEIGHT_BASE).
By default this parameter is disabled and no compensation will take place.
This parameter needs to be determined experimentally.
It is always better to set a conservative value (lower value) than an optimistic value.
### Apply Density Correction to Minimum Sink Rate
The minimum sink rate is set in [FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN).
If the [Basic TECS tuning](../config_fw/position_tuning_guide_fixedwing.md#tecs-tuning-altitude-and-airspeed) was not done in standard sea level conditions then the [FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN) parameter must be modified by multiplying with correction factor $P$ (where $\rho$ is the air density during tuning):
$$P = \sqrt{\rho\over{\rho_{sealevel}}}$$
For more information see [Effect of Density on minimum sink rate](#effect-of-density-on-minimum-sink-rate).
### Apply Density Correction to Trim Throttle
The trim throttle is set using [FW_THR_TRIM](../advanced_config/parameter_reference.md#FW_THR_TRIM).
If basic tuning was not done in standard sealevel conditions then the value for [FW_THR_TRIM](../advanced_config/parameter_reference.md#FW_THR_TRIM) must be modified by multiplying with correction factor $P$:
$$P = \sqrt{\rho\over{\rho_{sealevel}}}$$
For more information see [Effect of Density on Trim Throttle](#effect-of-density-on-trim-throttle)
## Weight and Density Compensation Algorithms
This section contains information about the scaling operations performed by PX4.
This is provided for interest only, and may be of interest to developers who want to modify the scaling code.
### 표기법
In the following sections we will use the notation $\hat X$ to specify that this value is a calibrated value of the variable $X$.
By calibrated we mean the value of that variable measured at sea level in standard atmospheric conditions, and when vehicle weight was equal to [WEIGHT_BASE](../advanced_config/parameter_reference.md#WEIGHT_BASE).
예: by $\hat{\dot{h}}_{max}$ we specify the maximum climb rate the vehicle can achieve at [WEIGHT_BASE](../advanced_config/parameter_reference.md#WEIGHT_BASE) at sea level in standard atmospheric conditions.
### Effect of Weight on Maximum Climb Rate
The maximum climb rate ([FW_T_CLMB_MAX](../advanced_config/parameter_reference.md#FW_T_CLMB_MAX)) is scaled as a function of the weight ratio.
From the steady state equations of motions of an airplane we find that the maximum climb rate can be written as:
$$\dot{h}_{max} = { V * ( Thrust - Drag ) \over{m*g}}$$
where `V` is the true airspeed and `m` is the vehicle mass.
From this equation we see that the maximum climb rates scales with vehicle mass.
### Effect of Weight on Minimum Sink Rate
The minimum sink rate ([FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN)) is scaled as a function of weight ratio
The minimum sink rate can be written as:
$$\dot{h}_{min} = \sqrt{2mg\over{\rho S}} f(C_L, C_D)$$
where $\rho$ is the air density, S is the wing surface reference area and $f(C_L, C_D)$ is a function of the polars, lift and drag.
From this equation we see that the minimum sink rate scales with the square root of the weight ratio.
### Effect of Weight on Airspeed Limits
The minimum airspeed ([FW_AIRSPD_MIN](../advanced_config/parameter_reference.md#FW_AIRSPD_MIN)), the stall airspeed ([FW_AIRSPD_STALL](../advanced_config/parameter_reference.md#FW_AIRSPD_STALL)) and trim airspeed ([FW_AIRSPD_TRIM](../advanced_config/parameter_reference.md#FW_AIRSPD_TRIM)) are adjusted based on the weight ratio specified by [WEIGHT_BASE](../advanced_config/parameter_reference.md#WEIGHT_BASE) and [WEIGHT_GROSS](../advanced_config/parameter_reference.md#WEIGHT_GROSS).
In steady state flight we can demand that lift should equal weight of the vehicle:
$$Lift = mg = {1\over{2}} \rho V^2 S C_L$$
rearranging this equation for airspeed gives:
$$V = \\sqrt{\\frac{2mg}{\\rho S C_D }}$$
From this equation we see that if we assume a constant angle of attack (which we generally desire), the vehicle weight affects airspeed with a square root relation.
Therefore, the airspeed limits mentioned above are all scaled using the square root of the weight ratio.
### Effect of Density on Maximum Climb Rate
The maximum climb rate is set using [FW_T_CLMB_MAX](../advanced_config/parameter_reference.md#FW_T_CLMB_MAX).
As we have seen previously, the maximum climb rate can be formulated as:
$$\dot{h}_{max} = { V * ( Thrust - Drag ) \over{m*g}}$$
The air density affects the airspeed, the thrust and the drag and modelling this effects is not straight forward.
However, we can refer to literature and experience, which suggest that for a propeller airplane the maximum climb rate reduces approximately linear with the air density.
Therefore, we can write the maximum climb rate as:
$$\dot{h}_{max} = \hat{\dot{h}} * {\rho_{sealevel} \over{\rho}} K$$
where $\rho_{sealevel}$ is the air density at sea level in the standard atmosphere and K is a scaling factor which determines the slope of the function.
Rather than trying to identify this constants, the usual practice in aviation is to specify a service ceiling altitude at which the vehicle is still able to achieve a minimum specified climb rate.
### Effect of Density on Minimum Sink Rate
The minimum sink rate is set using [FW_T_SINK_MIN](../advanced_config/parameter_reference.md#FW_T_SINK_MIN).
In previous sections we have seen the formula for the minimum sink rate:
$$\dot{h}_{min} = \sqrt{2mg\over{\rho S}} f(C_L, C_D)$$
This shows that the minimum sink rate scales with the square root of the inverse air density.
### Effect of Density on Trim Throttle
TODO: Add derivation here.