diff --git a/examples/parameter_example.yml b/examples/parameter_example.yml
index 892016d68a4423de585c75cc5041fb50690e944a..be2f512613edffd72eaf03689bccee0dd755726b 100644
--- a/examples/parameter_example.yml
+++ b/examples/parameter_example.yml
@@ -85,7 +85,7 @@ IsothermalPotential:
 DiscPatchPotential:
   surface_density: 10.      # Surface density of the disc (internal units)
   scale_height:    100.     # Scale height of the disc (internal units)
-  z_disc:          200.     # Disc height (internal units)
+  z_disc:          200.     # Position of the disc along the z-axis (internal units)
   timestep_mult:   0.03     # Dimensionless pre-factor for the time-step condition
   growth_time:     5.       # (Optional) Time for the disc to grow to its final size (multiple of the dynamical time)
 
diff --git a/src/gravity/Default/gravity.h b/src/gravity/Default/gravity.h
index 0f13f9557b7c72d73ed780d1280df8ae0b94d7cf..9e0ca81edff06b8a32afb185f24a88b41dc87da7 100644
--- a/src/gravity/Default/gravity.h
+++ b/src/gravity/Default/gravity.h
@@ -22,17 +22,14 @@
 
 #include <float.h>
 #include "minmax.h"
-#include "physical_constants.h"
 
 /**
  * @brief Computes the gravity time-step of a given particle due to self-gravity
  *
- * @param phys_const The physical constants in internal units.
  * @param gp Pointer to the g-particle data.
  */
 __attribute__((always_inline)) INLINE static float
-gravity_compute_timestep_self(const struct phys_const* const phys_const,
-                              const struct gpart* const gp) {
+gravity_compute_timestep_self(const struct gpart* const gp) {
 
   const float ac2 = gp->a_grav[0] * gp->a_grav[0] +
                     gp->a_grav[1] * gp->a_grav[1] +
diff --git a/src/potential/disc_patch/potential.h b/src/potential/disc_patch/potential.h
index 169e6d1e9007740a538941b57088f6d7ee022e27..21d168818e164ad3b3e18076ba824285e40956aa 100644
--- a/src/potential/disc_patch/potential.h
+++ b/src/potential/disc_patch/potential.h
@@ -35,14 +35,29 @@
 #include "physical_constants.h"
 #include "units.h"
 
-/* External Potential Properties */
+/**
+ * @brief External Potential Properties - Disc patch case
+ *
+ * See Creasey, Theuns & Bower, 2013, MNRAS, Volume 429, Issue 3, p.1922-1948
+ */
 struct external_potential {
 
+  /*! Surface density of the disc */
   double surface_density;
+
+  /*! Disc scale-height */
   double scale_height;
+
+  /*! Position of the disc along the z-axis */
   double z_disc;
+
+  /*! Dynamical time of the system */
   double dynamical_time;
+
+  /*! Time over which to grow the disk in units of the dynamical time */
   double growth_time;
+
+  /*! Time-step condition pre-factor */
   double timestep_mult;
 };
 
@@ -70,7 +85,7 @@ __attribute__((always_inline)) INLINE static float external_gravity_timestep(
   const float dz = fabs(g->x[2] - potential->z_disc);
 
   /* vertical cceleration */
-  const float z_accel = 2 * M_PI * phys_const->const_newton_G *
+  const float z_accel = 2.f * M_PI * phys_const->const_newton_G *
                         potential->surface_density *
                         tanh(dz / potential->scale_height);
 
@@ -92,7 +107,7 @@ __attribute__((always_inline)) INLINE static float external_gravity_timestep(
   float dt3 = FLT_MAX;
   if (abs(g->v_full[2]) > 0) {
     const float dz_accel_over_dt =
-        2 * M_PI * phys_const->const_newton_G * potential->surface_density /
+        2.f * M_PI * phys_const->const_newton_G * potential->surface_density /
         potential->scale_height / cosh(dz / potential->scale_height) /
         cosh(dz / potential->scale_height) * fabs(g->v_full[2]);
 
@@ -118,21 +133,20 @@ __attribute__((always_inline)) INLINE static void external_gravity_acceleration(
     double time, const struct external_potential* restrict potential,
     const struct phys_const* restrict phys_const, struct gpart* restrict g) {
 
-  const float G_newton = phys_const->const_newton_G;
   const float dz = g->x[2] - potential->z_disc;
   const float t_dyn = potential->dynamical_time;
 
-  float reduction_factor = 1.;
+  float reduction_factor = 1.f;
   if (time < potential->growth_time * t_dyn)
     reduction_factor = time / (potential->growth_time * t_dyn);
 
-  const float z_accel = reduction_factor * 2 * G_newton * M_PI *
+  /* Accelerations. Note that they are multiplied by G later on */
+  const float z_accel = reduction_factor * 2.f * M_PI *
                         potential->surface_density *
                         tanh(fabs(dz) / potential->scale_height);
 
-  /* Accelerations. Note that they are multiplied by G later on */
-  if (dz > 0) g->a_grav[2] -= z_accel / G_newton;
-  if (dz < 0) g->a_grav[2] += z_accel / G_newton;
+  if (dz > 0) g->a_grav[2] -= z_accel;
+  if (dz < 0) g->a_grav[2] += z_accel;
 }
 
 /**
@@ -149,16 +163,16 @@ static INLINE void potential_init_backend(
     const struct phys_const* phys_const, const struct UnitSystem* us,
     struct external_potential* potential) {
 
-  potential->surface_density =
-      parser_get_param_double(parameter_file, "DiscPatchPotential:surface_density");
-  potential->scale_height =
-      parser_get_param_double(parameter_file, "DiscPatchPotential:scale_height");
+  potential->surface_density = parser_get_param_double(
+      parameter_file, "DiscPatchPotential:surface_density");
+  potential->scale_height = parser_get_param_double(
+      parameter_file, "DiscPatchPotential:scale_height");
   potential->z_disc =
       parser_get_param_double(parameter_file, "DiscPatchPotential:z_disc");
-  potential->timestep_mult =
-      parser_get_param_double(parameter_file, "DiscPatchPotential:timestep_mult");
-  potential->growth_time =
-      parser_get_opt_param_double(parameter_file, "DiscPatchPotential:growth_time", 0.);
+  potential->timestep_mult = parser_get_param_double(
+      parameter_file, "DiscPatchPotential:timestep_mult");
+  potential->growth_time = parser_get_opt_param_double(
+      parameter_file, "DiscPatchPotential:growth_time", 0.);
   potential->dynamical_time =
       sqrt(potential->scale_height /
            (phys_const->const_newton_G * potential->surface_density));
@@ -179,7 +193,7 @@ static INLINE void potential_print_backend(
       potential->timestep_mult);
 
   if (potential->growth_time > 0.)
-    message("Disc will grow for %f dynamiccal times.", potential->growth_time);
+    message("Disc will grow for %f dynamical times.", potential->growth_time);
 }
 
 #endif /* SWIFT_DISC_PATCH_H */
diff --git a/src/potential/isothermal/potential.h b/src/potential/isothermal/potential.h
index 4a43f0d344c52fd5afeb6b75ce8ef75deee343e2..a993c09a978ca3692ec3359f7633df14760f263d 100644
--- a/src/potential/isothermal/potential.h
+++ b/src/potential/isothermal/potential.h
@@ -33,12 +33,22 @@
 #include "physical_constants.h"
 #include "units.h"
 
-/* External Potential Properties */
+/**
+ * @brief External Potential Properties - Isothermal sphere case
+ */
 struct external_potential {
 
+  /*! Position of the centre of potential */
   double x, y, z;
+
+  /*! Rotation velocity */
   double vrot;
-  float timestep_mult;
+
+  /*! Square of vrot divided by G \f$ \frac{v_{rot}^2}{G} \f$ */
+  double vrot2_over_G;
+
+  /*! Time-step condition pre-factor */
+  double timestep_mult;
 };
 
 /**
@@ -65,11 +75,11 @@ __attribute__((always_inline)) INLINE static float external_gravity_timestep(
   const double vrot = potential->vrot;
 
   const float dota_x =
-      vrot * vrot * rinv2 * (g->v_full[0] - 2 * drdv * dx * rinv2);
+      vrot * vrot * rinv2 * (g->v_full[0] - 2.f * drdv * dx * rinv2);
   const float dota_y =
-      vrot * vrot * rinv2 * (g->v_full[1] - 2 * drdv * dy * rinv2);
+      vrot * vrot * rinv2 * (g->v_full[1] - 2.f * drdv * dy * rinv2);
   const float dota_z =
-      vrot * vrot * rinv2 * (g->v_full[2] - 2 * drdv * dz * rinv2);
+      vrot * vrot * rinv2 * (g->v_full[2] - 2.f * drdv * dz * rinv2);
   const float dota_2 = dota_x * dota_x + dota_y * dota_y + dota_z * dota_z;
   const float a_2 = g->a_grav[0] * g->a_grav[0] + g->a_grav[1] * g->a_grav[1] +
                     g->a_grav[2] * g->a_grav[2];
@@ -92,14 +102,12 @@ __attribute__((always_inline)) INLINE static void external_gravity_acceleration(
     double time, const struct external_potential* potential,
     const struct phys_const* const phys_const, struct gpart* g) {
 
-  const double G_newton = phys_const->const_newton_G;
   const float dx = g->x[0] - potential->x;
   const float dy = g->x[1] - potential->y;
   const float dz = g->x[2] - potential->z;
   const float rinv2 = 1.f / (dx * dx + dy * dy + dz * dz);
 
-  const double vrot = potential->vrot;
-  const double term = -vrot * vrot * rinv2 / G_newton;
+  const double term = -potential->vrot2_over_G * rinv2;
 
   g->a_grav[0] += term * dx;
   g->a_grav[1] += term * dy;
@@ -130,6 +138,9 @@ static INLINE void potential_init_backend(
       parser_get_param_double(parameter_file, "IsothermalPotential:vrot");
   potential->timestep_mult = parser_get_param_float(
       parameter_file, "IsothermalPotential:timestep_mult");
+
+  potential->vrot2_over_G =
+      potential->vrot * potential->vrot / phys_const->const_newton_G;
 }
 
 /**
diff --git a/src/potential/point_mass/potential.h b/src/potential/point_mass/potential.h
index 7d794347cb66c7a1e1fc864620d1f8ac25a5a269..f718af2e2c4ff91540e1834cb2072d321ce38705 100644
--- a/src/potential/point_mass/potential.h
+++ b/src/potential/point_mass/potential.h
@@ -34,12 +34,17 @@
 #include "units.h"
 
 /**
- * @brief External Potential Properties
+ * @brief External Potential Properties - Point mass case
  */
 struct external_potential {
 
+  /*! Position of the point mass */
   double x, y, z;
+
+  /*! Mass */
   double mass;
+
+  /*! Time-step condition pre-factor */
   float timestep_mult;
 };