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(* -*- mode: tuareg; -*- *)
type naca4_num = string
type naca4_params = { m : float; p : float; t : float }
type coord = Coordinate of { x : float; y : float }
type naca4_coords = { c : coord array; u : coord array; l : coord array }
type naca4_arfoil = { naca_num : naca4_num; coords : naca4_coords }
let get_params naca_num =
if String.length naca_num <> 4 then
raise (Invalid_argument "NACA number must be a 4-digit string");
(* Maximum camber *)
let m = String.sub naca_num 0 1 |> float_of_string |> ( *. ) 0.01 in
(* Location of maximum camber *)
let p = String.sub naca_num 1 1 |> float_of_string |> ( *. ) 0.10 in
(* Maximum thickness *)
let t = String.sub naca_num 2 2 |> float_of_string |> ( *. ) 0.01 in
{ m; p; t }
let y_t t x =
5. *. t
*. ((0.2969 *. sqrt x)
-. (0.1260 *. x)
-. (0.3516 *. (x ** 2.))
+. (0.2843 *. (x ** 3.))
-. (0.1015 *. (x ** 4.)))
let array_of_amt amt =
Array.init (amt + 1) (fun x -> float_of_int x /. float_of_int amt)
let densified_array_of_amt amt =
let pct = 0.25 in
let dense_amt = int_of_float (pct *. float_of_int amt) in
let factor = 5. in
let dense_array =
Array.init
(int_of_float (pct *. amt *. factor))
(fun x -> float_of_int x /. (10. *. factor))
in
let sparse_array =
let pct = 1. -. pct in
Array.init
(int_of_float (pct *. (amt)))
(fun x -> (float_of_int x +. (pct *. factor)) /. factor)
in
Array.append dense_array sparse_array
(* Symmetrical airfoil *)
module Symmetrical = struct
let center_coord x = Coordinate { x; y = 0. }
let upper_coord t x =
let y = y_t x t in
Coordinate { x; y }
let lower_coord t x =
let y = -.y_t x t in
Coordinate { x; y }
let get_coords t xs =
{
c = Array.map center_coord xs;
u = Array.map (upper_coord t) xs;
l = Array.map (lower_coord t) xs;
}
end
(* Cambered airfoil *)
module Cambered = struct
let y_c m p x =
if 0. <= x && x <= p then m /. (p ** 2.) *. ((2. *. p *. x) -. (x ** 2.))
else if p <= x && x <= 1. then
m /. ((1. -. p) ** 2.) *. (1. -. (2. *. p) +. (2. *. p *. x) -. (x ** 2.))
else failwith "x value out of bounds"
let theta m p x =
let dy_c_over_dx =
if 0. <= x && x <= p then 2. *. m /. (p ** 2.) *. (p -. x)
else if p <= x && x <= 1. then 2. *. m /. ((1. -. p) ** 2.) *. (p -. x)
else failwith "x value out of bounds"
in
atan dy_c_over_dx
let camber_coord m p x =
let y = y_c m p x in
Coordinate { x; y }
let upper_coord m p t x =
let y_t = y_t t x in
let y_c = y_c m p x in
let theta = theta m p x in
let x = x -. (y_t *. sin theta) in
let y = y_c +. (y_t *. cos theta) in
Coordinate { x; y }
let lower_coord m p t x =
let y_t = y_t t x in
let y_c = y_c m p x in
let theta = theta m p x in
let x = x +. (y_t *. sin theta) in
let y = y_c -. (y_t *. cos theta) in
Coordinate { x; y }
let get_coords m p t xs =
{
c = Array.map (camber_coord m p) xs;
u = Array.map (upper_coord m p t) xs;
l = Array.map (lower_coord m p t) xs;
}
end
let get_coords naca_num ?(amt = 100) () =
let { m; p; t } = get_params naca_num in
let x_coords = densified_array_of_amt amt in
let airfoil_is_symmetrical = m = 0. && p = 0. in
if airfoil_is_symmetrical then Symmetrical.get_coords t x_coords
else Cambered.get_coords m p t x_coords
let extract_coords coords =
let get_x (Coordinate c) = c.x in
let get_y (Coordinate c) = c.y in
let xs = Array.map get_x coords in
let ys = Array.map get_y coords in
(xs, ys)
let plot_curve coords =
let get_x (Coordinate c) = c.x in
let get_y (Coordinate c) = c.y in
let xs = Array.map get_x coords in
let ys = Array.map get_y coords in
(xs, ys)
let plot_airfoil naca_num ?(amt = 100) () =
let naca_coords = get_coords naca_num ~amt () in
let xs, ys = extract_coords naca_coords.c in
Plplot.plcol0 1;
Plplot.plpoin xs ys 1;
let xs, ys = extract_coords naca_coords.u in
Plplot.plcol0 6;
Plplot.plline xs ys;
let xs, ys = extract_coords naca_coords.l in
Plplot.plcol0 6;
Plplot.plline xs ys
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