the Hortens design their aircraft
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.
Wing Section Design
Wing 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.
Camber lines were designed by Birnbaum’s thin aerofoil theory to give zero
Cmo. This gives an equation for the case of 3% maximum camber:
y = 0.1055 x (1 – x)3
This has dx and dx2 both zero at x = 1 and gives y = max at x = 0.25
For fairing shapes with maximum thickness at 40% they used a geometrical
projection method due to Ringleb.
To get good stalling characteristics the following criterion was used:
(t/c)2 = 1.0
Where p = nose radius
c = chord
t = maximum thickness
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.
Horten thought that position of the maximum thickness of the wing section
had a definite influence on the sweepback that could be used (and
vice-versa) due to the influence on lateral flow in the boundary layer. He
suggested that following rough rule for 12% thick sections
Max Thickness Maximum Sweep
Location (Leading Edge)
This rule was based on his experience of the flying qualities of aircraft
so far built.
Calculation of Aerodynamic Centres
Aerodynamic centre was calculated by integration of the product of local
loading x distance of the local aerodynamic centre 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 centre 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:
Centre 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:
(ed. – top line of equation is Py dy.)
Py is the fore and aft distance between the aerodynamic centre of the
centre section and the aerodynamic centre at the general point y.
Fixing the Layout
Preliminary Determination of CG Position
As a first approximation Horten used the following graphical construction
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 above.
It will be noticed that the mean chord used by Horten is the local chord
line passing through the centre of area of the half wing. The above
construction does not apply to planforms differing greatly from a
trapezium. The chord length so defined is not the same as that given by s
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.
Where Delta = mean twist
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
Type (% p) Comments
III 4% Normal position
2% Minimum for satisfactory longitudinal stability
5% For best longitudinal characteristics
3% For optimum performance
IV 5% Normal
6-7% Best Handling
V, VII, IX 2-3%
On 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.
Centre section head fairing were found to have an appreciable effect on
In the case of high speed aircraft, selection of mean twist was farther
complicated by the need to avoid local shock stall at high speed. The
method of dealing with this was described in para. 3.11 under “Aerodynamic
Twist distribution was determined by the type of aircraft. For a
sailplane, which spends much of its time in circling flight, Horten had
developed a theory which enabled twist distribution to be designed so that
the glider was in trim laterally and directionally without elevon or
rudder deflection. In the calculation the twist needed to give static
equilibrium was found, taking into account variation of incidence, speed,
profile and induced drag across the span and assuming straight trailing
The answer was a twist of the form
e = eo ( A s + B ( s )3 )
(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
y ( y)2 ( y)3
e = 2° ( s + s + s )
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).
On the H III the linear term was much bigger (4°) and the incidence
difference between the tips 6° in the specified circling condition.
Torsional deflection of the wing was allowed for in these calculations.
In addition to the above requirements Horten also designs the combination
of taper and twist to ensure that local stalling lift coefficient is first
reached at the middle third of the semi span. Apparently all those
conditions can be satisfied simultaneously, the linear term was said to be
available mainly for stall control whilst the cubic term gave the required
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.
His calculations of control forces were customary, design was governed by
experience. Aileron performance was however calculated on the H IX.
The change over from round nosed to Frise nosed controls was made to
improve the yawing characteristics with aileron applications. The
subdivision of the flap into two parts enabled differential to be used to
improve the favourable yaw with aileron. The outer Frise nose in this case
balanced the round nosed inner flap also. In the three stage flap, where
the outer flap behaved principally as up going aileron, it was possible to
alter the relative balance between aileron and elevator (the latter being
usually too light relative to the aileron) and produce better harmony of
control. This was aid to be especially important in high aspect ratio
sailplanes (or airplanes ling the H VIII) where the ratio of lateral
inertia to longitudinal inertia is high (e.g. this ratio was about 30 on
the H VI compared with 5 on the H IX). Further questioning revealed that
Horten thought lateral inertia important because the initial response
(acceleration) when correcting small gust disturbances depended largely on
inertia although the final rate of roll was hardly affected.
Drag rudder design was evolved entirely by flight experiment with no wing
tunnel data to help.
Dynamic 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
The Hortens were obviously not in the habit of thinking in terms of
periods and dampings, and Reimar did not know that lv and nv were for his
various designs; dihedral was fixed by experience.
The “stick force per g” criterion was not used and although elevator
angles to trim were considered in the design stage there was no methodical
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 8 55 15
Main Wheel Reaction 92 45 85
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
According to Horten none of the layouts tested had given any trouble due
to porporsing or instability to unstick; he was inclined to dismiss
undercarriage design as presenting no problems.
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.
Actual figures quoted were:
1.5 mm Ply 2.5 mm Ply
Dive +3° +2.5°
4g Pullout +2.7° -0.5°