From 87029295c130bb3213847de37e355306da06dcd5 Mon Sep 17 00:00:00 2001
From: Julian Smith <jules@op59.net>
Date: Sat, 22 Jul 2023 19:10:15 +0100
Subject: [PATCH] src/FDM/YASim/: added optional quadratic term `spring2` to
 gear spring equation.

In YASim XML <gear>, `spring2` is a new dimensionless term. Default
value zero is backwards compatible. The new spring force equation is:

    force = _spring * compression * (_frac + spring2 * _frac**2)

This is intended to help with
https://sourceforge.net/p/flightgear/codetickets/1509.
---
 src/FDM/YASim/FGFDM.cpp | 1 +
 src/FDM/YASim/Gear.cpp  | 7 ++++++-
 src/FDM/YASim/Gear.hpp  | 2 ++
 3 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/src/FDM/YASim/FGFDM.cpp b/src/FDM/YASim/FGFDM.cpp
index 7d071d4d1..858f3f3a9 100644
--- a/src/FDM/YASim/FGFDM.cpp
+++ b/src/FDM/YASim/FGFDM.cpp
@@ -1090,6 +1090,7 @@ void FGFDM::parseGear(const XMLAttributes* a)
     g->setStaticFriction(attrf(a, "sfric", 0.8));
     g->setDynamicFriction(attrf(a, "dfric", 0.7));
     g->setSpring(attrf(a, "spring", 1));
+    g->setSpring2(attrf(a, "spring2", 0));
     g->setDamping(attrf(a, "damp", 1));
     if(a->hasAttribute("on-water")) g->setOnWater(attrb(a,"on-water"));
     if(a->hasAttribute("on-solid")) g->setOnSolid(attrb(a,"on-solid"));
diff --git a/src/FDM/YASim/Gear.cpp b/src/FDM/YASim/Gear.cpp
index c4c855f5f..ad48993d7 100644
--- a/src/FDM/YASim/Gear.cpp
+++ b/src/FDM/YASim/Gear.cpp
@@ -53,6 +53,7 @@ Gear::Gear()
     for(i=0; i<3; i++)
         _pos[i] = _stuck[i] = 0;
     _spring = 1;
+    _spring2 = 0;
     _damp = 0;
     _sfric = 0.8f;
     _dfric = 0.7f;
@@ -501,7 +502,11 @@ void Gear::calcForce(Ground *g_cb, RigidBody* body, State *s, float* v, float* r
         frac_with_initial_load = (_frac+_initialLoad)
             *_frac*_frac*3*25-_frac*_frac*_frac*2*125;
 
-    float fmag = frac_with_initial_load*clen*_spring;
+    float fmag = clen * _spring *
+            (
+            frac_with_initial_load
+            + _spring2 * pow( frac_with_initial_load, 2)
+            );
     if (_speed_planing>0)
     {
         float v = Math::mag3(cv);
diff --git a/src/FDM/YASim/Gear.hpp b/src/FDM/YASim/Gear.hpp
index 7c2370a6a..96ce0588d 100644
--- a/src/FDM/YASim/Gear.hpp
+++ b/src/FDM/YASim/Gear.hpp
@@ -67,6 +67,7 @@ public:
     
     void setSpring(float spring) { _spring = spring; }
     float getSpring() { return _spring; }
+    void setSpring2(float spring2) { _spring2 = spring2; }
     void setDamping(float damping) { _damp = damping; }
     float getDamping() {return _damp; }
     void setStaticFriction(float sfric) { _sfric = sfric; }
@@ -142,6 +143,7 @@ private:
     double _stuck[3] = {0};
     GearVector _cmpr;
     float _spring = 0;
+    float _spring2 = 0;
     float _damp = 0;
     float _sfric = 0;
     float _dfric = 0;