The Horten Tailless Aircraft
by K.G. Wilkinson, B.Sc. D.I.C.
How the Hortens Design Their
The Hortens started their careers as aircraft designers in a very practical way, without assistance from highbrow theory. Early designs were based mainly on what they found satisfactory on a small-scale model. As time went on Reimar Horten began theoretical investigations of various problems that took his fancy and built up a fairly complex basic design procedure. Some of his methods seem strange to us and some important aspects he still leaves to “experience” where we tend to trust theory. The following is a brief account of his methods as related to us at Gottingen in September 1945.
4.1 Wing Section Design
sections were designed from scratch and were never wind tunnel tested.
The only exception to this rule was the disastrous adoption of the Mustang
profile for the H IVb and the H XII.
To get good stalling characteristics the following criterion was used:
Where p = nose
This criterion is well known and a report by Kawalki of D.V.L. has been published on the subject.
Wing tip sections
are made symmetrical because Horten dislikes the idea of a cambered section
with negative flap deflection at the stall.
Max Thickness Maximum Sweep
This rule was based on his experience of the flying qualities of aircraft so far built.
4.2 Calculation of Aerodynamic Centers
Aerodynamic center was calculated by integration of the product of local loading x distance of the local aerodynamic center behind a convenient spanwise datum. Load distribution was first calculated by Weissingers method for a sweptback wing. Details of this were not known but it was apparently a development of Multopp’s method which extended the lifting line theory to take account of chordwise pressure distribution and the influence of this on induced velocity along the span. Load distribution was used to give values of
d CL local
Local aerodynamic center was assumed to be at
0.25 x n x C from the leading edge, n being a factor representing the departure
of the two-dimensional lift curve slope from 2 pi.
n had approximately the following values for different thickness ratios:
Center of gravity positions were specified by Horten as distances ahead of the above neutral point in terms of a dimension called the “Pfeilmass”. The Pfeilmass is a measure of the fore and aft dimension of the wing and is defined by:
Py is the fore and aft distance between the aerodynamic center of the center section and the aerodynamic center at the general point y.
4.3 Fixing the Layout
Preliminary Determination of CG Position
As a first approximation Horten used the following graphical contstruction to give a mean chord and mean quarter chord point.
The first approximation
to the CG position was taken as the man quarter chord point defined as
The procedure here was to construct curves from which static margin could be chosen if wing twist had been decided, or, more usually, to choose twist for a given static margin, assuming in either case that the desired CL with elevons neutral was known.
Deltay = twist at general point y
Cy = chord at general point y
S = wing area
s = semi span
Desirable static margins were known from experience and Horten gave the following table (all in % of Pfeilmass) of values for different Horten aircraft.
sailplanes, twist was designed to give elevon neutral trim near to the
CL for best gliding angle and on power aircraft trim at cruising
CL. Center section head fairing were found to have an
appreciable effect on trim.
(ed. – missing text about one of the terms being indeterminate.)
On the H IV for example, twist was designed to give trim in a 45° banked turn at CL = 1. Incidence difference between the tips was 1° and the twist was
y ( y)2 (
An additional aerodynamic
twist of 1.1° was added giving an overall designed washout of 7.1°.
The second power term was introduced to satisfy the condition for longitudinal
trim (flaps neutral for trimmed flight at 100 kph on the H IV and 140 kph
on the H VI).
Sweepback is governed to some extent by the load being carried, but for low speed aircraft Horten liked to keep leading edge sweepback below 45° to avoid loss of controller power through boundary layer outflow. For high speed aircraft, high sweepback was an advantage, for besides keeping drag down it prevented over sensitivity of control.
4.4 Control Design
of control forces were customary, design was governed by experience.
Aileron performance was however calculated on the H IX.
4.5 Flight Stability
was never investigated theoretically and was not studied very carefully
in flight. Reliance was placed mainly on general impressions of the
pilot and we found no evidence of results having been analyzed critically.
4.6 Undercarriage Design
During the construction of their series of aircraft the Hortens had been forced to try a number of unorthodox undercarriage layouts using 2, 3 and 4 wheels. The tricycle and four wheel layouts used wheel positions giving a wide range of weight distribution. The following figures were quoted:
Type H IV H V H VIII
Nose Wheel Reaction
The H VII and H IX also
take a large proportion of the weight on the nosewheel – of the order 40-50%.
These heavy nosewheel reactions were combined with large ground incidence
to enable the aircraft to fly off the ground.
Horten stated that there were no special requirements for stress calculations on tailless aircraft. The H IX was designed for a normal acceleration (n) of 7g combined with a safety factor (j) of 1.8. Other design considerations were as follows:
(a) Gusts of + 10 m/sec. in a dive at 1100 kph with j = 1.2. The air was assumed incompressible for this calculation except that dCL / da was arbitrarily increased 50% over the incompressible value. A relieving factor of 0.6 was applied.
(b) A complete aileron roll (360°) was to be possible at 900 kph at 2500 m. in 4 seconds, including allowance for aero elastic distortion. This was both a performance and a stressing requirement.
(c) There were no official aileron reversal requirements but Hortens designed the H IX for a reversal speed of 1.2 x diving speed (1320 kph) assuming incompressible flow.
A peculiar feature
in the structural design of the H VII was mentioned. It was stated
that the calculated change of trim to cause a 4g dive pull out at diving
speed was only 0.3° of elevon, when allowance was made for aero elastic
distortion. This was improved by increasing the ply skin thickness
from 1.5 mm to 2.5 mm. The phenomenon would be more understandable
if the torsion component of spar bending had been large but Horten says
that this was not included.