diff --git a/aircraft_cmd.c b/aircraft_cmd.c
index f74d92ec2c..ba1c9ee2b1 100644
--- a/aircraft_cmd.c
+++ b/aircraft_cmd.c
@@ -764,7 +764,7 @@ static bool AircraftController(Vehicle *v)
 	Station *st;
 	const AirportMovingData *amd;
 	Vehicle *u;
-	byte z,dirdiff,newdir,maxz,curz;
+	byte z,newdir,maxz,curz;
 	GetNewVehiclePosResult gp;
 	uint dist;
 	int x,y;
@@ -853,20 +853,22 @@ static bool AircraftController(Vehicle *v)
 
 	// At final pos?
 	if (dist == 0) {
+		DirDiff dirdiff;
+
 		if (v->cur_speed > 12) v->cur_speed = 12;
 
 		// Change direction smoothly to final direction.
-		dirdiff = amd->direction - v->direction;
+		dirdiff = DirDifference(amd->direction, v->direction);
 		// if distance is 0, and plane points in right direction, no point in calling
 		// UpdateAircraftSpeed(). So do it only afterwards
-		if (dirdiff == 0) {
+		if (dirdiff == DIRDIFF_SAME) {
 			v->cur_speed = 0;
 			return true;
 		}
 
 		if (!UpdateAircraftSpeed(v)) return false;
 
-		v->direction = (v->direction+((dirdiff&7)<5?1:-1)) & 7;
+		v->direction = ChangeDir(v->direction, dirdiff > DIRDIFF_REVERSE ? DIRDIFF_45LEFT : DIRDIFF_45RIGHT);
 		v->cur_speed >>= 1;
 
 		SetAircraftPosition(v, v->x_pos, v->y_pos, v->z_pos);
diff --git a/direction.h b/direction.h
index e29fb3c49c..4aed8bea30 100644
--- a/direction.h
+++ b/direction.h
@@ -23,6 +23,32 @@ static inline Direction ReverseDir(Direction d)
 }
 
 
+typedef enum DirDiff {
+	DIRDIFF_SAME    = 0,
+	DIRDIFF_45RIGHT = 1,
+	DIRDIFF_90RIGHT = 2,
+	DIRDIFF_REVERSE = 4,
+	DIRDIFF_90LEFT  = 6,
+	DIRDIFF_45LEFT  = 7
+} DirDiff;
+
+static inline DirDiff DirDifference(Direction d0, Direction d1)
+{
+	return (DirDiff)(d0 + 8 - d1) % 8;
+}
+
+static inline DirDiff ChangeDirDiff(DirDiff d, DirDiff delta)
+{
+	return (DirDiff)((d + delta) % 8);
+}
+
+
+static inline Direction ChangeDir(Direction d, DirDiff delta)
+{
+	return (Direction)((d + delta) % 8);
+}
+
+
 /* Direction commonly used as the direction of entering and leaving tiles, 4-way */
 typedef enum DiagDirection {
 	DIAGDIR_NE  = 0,      /* Northeast, upper right on your monitor */
diff --git a/train_cmd.c b/train_cmd.c
index 49c186e8f9..960af695a8 100644
--- a/train_cmd.c
+++ b/train_cmd.c
@@ -2591,14 +2591,16 @@ static const RailtypeSlowdownParams _railtype_slowdown[3] = {
 /* Modify the speed of the vehicle due to a turn */
 static void AffectSpeedByDirChange(Vehicle* v, Direction new_dir)
 {
-	byte diff;
+	DirDiff diff;
 	const RailtypeSlowdownParams *rsp;
 
-	if (_patches.realistic_acceleration || (diff = (v->direction - new_dir) & 7) == 0)
-		return;
+	if (_patches.realistic_acceleration) return;
+
+	diff = DirDifference(v->direction, new_dir);
+	if (diff == DIRDIFF_SAME) return;
 
 	rsp = &_railtype_slowdown[v->u.rail.railtype];
-	v->cur_speed -= ((diff == 1 || diff == 7) ? rsp->small_turn : rsp->large_turn) * v->cur_speed >> 8;
+	v->cur_speed -= (diff == DIRDIFF_45RIGHT || diff == DIRDIFF_45LEFT ? rsp->small_turn : rsp->large_turn) * v->cur_speed >> 8;
 }
 
 /* Modify the speed of the vehicle due to a change in altitude */
@@ -2739,11 +2741,10 @@ static void *CheckVehicleAtSignal(Vehicle *v, void *data)
 {
 	const VehicleAtSignalData* vasd = data;
 
-	if (v->type == VEH_Train && IsFrontEngine(v) &&
-			v->tile == vasd->tile) {
-		byte diff = (v->direction - vasd->direction + 2) & 7;
+	if (v->type == VEH_Train && IsFrontEngine(v) && v->tile == vasd->tile) {
+		DirDiff diff = ChangeDirDiff(DirDifference(v->direction, vasd->direction), DIRDIFF_90RIGHT);
 
-		if (diff == 2 || (v->cur_speed <= 5 && diff <= 4)) return v;
+		if (diff == DIRDIFF_90RIGHT || (v->cur_speed <= 5 && diff <= DIRDIFF_REVERSE)) return v;
 	}
 	return NULL;
 }
diff --git a/vehicle.c b/vehicle.c
index e4dd53774f..24d7b731f6 100644
--- a/vehicle.c
+++ b/vehicle.c
@@ -1930,7 +1930,7 @@ static const Direction _new_direction_table[] = {
 Direction GetDirectionTowards(const Vehicle* v, int x, int y)
 {
 	Direction dir;
-	byte dirdiff;
+	DirDiff dirdiff;
 	int i = 0;
 
 	if (y >= v->y_pos) {
@@ -1945,10 +1945,9 @@ Direction GetDirectionTowards(const Vehicle* v, int x, int y)
 
 	dir = v->direction;
 
-	dirdiff = _new_direction_table[i] - dir;
-	if (dirdiff == 0)
-		return dir;
-	return (dir+((dirdiff&7)<5?1:-1)) & 7;
+	dirdiff = DirDifference(_new_direction_table[i], dir);
+	if (dirdiff == DIRDIFF_SAME) return dir;
+	return ChangeDir(dir, dirdiff > DIRDIFF_REVERSE ? DIRDIFF_45LEFT : DIRDIFF_45RIGHT);
 }
 
 Trackdir GetVehicleTrackdir(const Vehicle* v)