A high-voltage cable assembly that passes sea-level testing cannot be assumed to perform safely at altitude. As air pressure falls, gas breakdown voltage changes nonlinearly with the pressure-gap product — and the worst-case altitude for corona inception is often not the highest altitude. The physics is well established, the failure modes are predictable, and they can usually be prevented or detected with the correct design and qualification approach.
Altitude performance · 10 kV–250 kV DC · Aerospace, defense, high-altitude UAV
The relationship between gas pressure, electrode gap, and electrical breakdown voltage was characterized empirically by Friedrich Paschen in 1889. Paschen's Law states that the breakdown voltage of a gas is a function of the product of pressure (p) and gap distance (d) — not of pressure or gap distance independently. This has two important consequences for high-voltage assembly design.
First: as pressure decreases at constant gap, the pd product decreases. Over part of the Paschen curve, this lowers the breakdown voltage — so an air gap that is acceptable at sea level may have substantially less corona / breakdown margin at altitude. The amount of reduction cannot be predicted by a simple linear pressure correction; it depends on the effective gap dimension, gas composition, electrode geometry, surface condition, and field uniformity. Under a standard-atmosphere model, ambient pressure at 70,000 ft is approximately 4.4 kPa — roughly 4% of sea-level pressure (101.3 kPa) — and the dielectric margin of any unresolved air gap at this pressure can be a small fraction of the sea-level value.
Second, and less intuitively: the relationship is not monotonic. The Paschen curve has a minimum — a specific pd value at which breakdown voltage is lowest. Below that minimum, as pressure decreases further, breakdown voltage rises again. This means that for practical gap geometries in an aircraft assembly, there exists a specific altitude at which corona inception voltage is at its minimum, and that altitude may be well below the maximum operating altitude.
The Physics Behind the Paschen Curve
Gas breakdown via the Townsend avalanche mechanism requires that electrons accelerated by the electric field gain sufficient energy between collisions to ionize gas molecules, generating secondary electrons that sustain the discharge. At high pressure, frequent collisions prevent electrons from accumulating enough energy — breakdown voltage is high. At very low pressure, mean free path becomes long and electrons travel far between collisions, again requiring higher voltage to sustain an avalanche — breakdown voltage rises. At intermediate pressure, the collision rate and electron energy are optimally matched for avalanche initiation — this is the Paschen minimum. The pressure at which the minimum occurs is a function of the pressure-gap product (pd), so the equivalent altitude depends directly on the effective gap dimension. For small interface gaps in connector geometries, the minimum may fall in the pressure range corresponding to high aircraft altitudes; for larger gaps, the minimum occurs at much lower pressures. There is no universal "Paschen minimum altitude."
Several terms are used loosely in this domain and are worth stating precisely, because the distinctions affect how tests are specified and interpreted.
The connector mating interface is the most altitude-sensitive location in a typical high-voltage cable assembly. In most conventional connector designs, the interface between the male and female insulation bodies is not perfectly conformal — some air is present at the interface, whether by design or by the dimensional tolerances of assembled parts. At sea level, this air gap may have adequate dielectric strength for the operating voltage. At altitude, the same gap has a fraction of its sea-level dielectric strength.
Caton's tapered conical mating geometry is specifically designed to address this mechanism. When the plug engages the receptacle, the tapered geometry progressively displaces air from the interface as the mating surfaces come into contact. The design objective is a controlled solid-dielectric interface with no uncontrolled air gap in the high-field region — so that corona inception behavior at altitude is governed by the solid insulation rather than a trapped air gap. Altitude performance is then verified by test under defined voltage, pressure, and mating conditions.
Any air void in the termination region — in potting compound, at the cable-to-connector insulation interface, or at the shield cutback — is altitude-sensitive. Voids that are electrically inactive at sea level, because the field intensity in the trapped air is below the sea-level breakdown threshold, may become active corona sites at altitude when the same field intensity exceeds the reduced breakdown threshold of the lower-pressure air.
This is why altitude testing cannot substitute for void control. Testing at altitude will detect voids that produce corona — but corona in the termination region indicates a design or fabrication problem, not a margin that can be managed by limiting operating conditions. The correct design objective is to avoid air-filled voids in electrically stressed regions, minimize trapped gas at interfaces, and verify adequate corona / PD margin under the relevant pressure conditions.
For assemblies with insufficient outer insulation thickness, or with sharp external features that concentrate the external fringing field, external corona can occur in the air surrounding the assembly at altitude even if the internal insulation system is well-controlled. The field at the outer surface is determined by the insulation geometry and the operating voltage. At altitude, the threshold for corona inception in the surrounding air falls — and assemblies with marginal external field control may exhibit external corona at altitude that is not present at sea level.
Critical Design Point — The Paschen Minimum Is Not at Maximum Altitude
For many practical high-voltage assemblies, the lowest corona inception voltage occurs at an intermediate pressure — not necessarily at the highest operating altitude. The pressure at which the Paschen minimum occurs depends on the effective gap dimension in the specific design, and may fall within, below, or above the rated operating altitude range. An assembly qualified only at sea level and maximum altitude may not have been evaluated at the worst-case condition. RTCA DO-160G Section 4 altitude categories peak at 70,000 ft; qualification testing for high-voltage assemblies intended to fly through or operate near reduced-pressure environments should include the pressure range corresponding to credible worst-case gaps, not only the test endpoints.
The table below shows representative ambient pressure at several altitudes. The relationship between pressure and air dielectric strength is not strictly linear — the Paschen curve captures the nonlinear behavior — but the pressure values illustrate the order-of-magnitude reduction that is relevant to design margins.
| Altitude | Approx. Pressure | % of Sea Level | Design Implication |
|---|---|---|---|
| Sea level | 101.3 kPa / 760 torr | 100% | Baseline. Sea-level corona testing defines minimum performance only. |
| 15,000 ft | 57.2 kPa / 429 torr | 56% | Pressurized cabin equivalent per DO-160 Category A. Air dielectric strength reduced but well above Paschen minimum for most credible gaps. |
| 35,000 ft | 23.8 kPa / 179 torr | 24% | Typical commercial cruise altitude. Unpressurized bays may be at this pressure. |
| 50,000 ft | 11.6 kPa / 87 torr | 11.4% | High-altitude UAV and reconnaissance regime. Approaches Paschen minimum for some larger gap geometries. |
| 70,000 ft | 4.4 kPa / 33 torr | 4.4% | RTCA DO-160 maximum altitude category. Paschen minimum regime for credible mm-scale interface gaps in many connector designs — evaluate explicitly for the specific gap geometry. |
| 80,000 ft | 2.8 kPa / 21 torr | 2.7% | Unpressurized high-altitude regime. May correspond to Paschen minimum for smaller interface gaps. |
| 100,000 ft | 1.1 kPa / 8 torr | 1.1% | Breakdown voltage rises on left side of Paschen curve for many gap sizes. Space systems may operate in this regime; design per NASA-HDBK-4007A. |
Pressure values calculated from the U.S. Standard Atmosphere 1976 (ISA). The Paschen minimum pressure depends on the specific gap geometry and gas composition — there is no universal Paschen-minimum altitude. Assemblies with credible air gaps in the high-field region should be evaluated at the pressure range corresponding to the worst-case pd for that gap, in addition to sea-level and maximum-altitude endpoints.
A corona inception voltage measurement taken at sea level characterizes the insulation system at 101.3 kPa. It does not provide a basis for predicting PDIV at reduced pressure, for two reasons.
First, the Paschen curve is nonlinear. There is no simple scaling factor from sea-level PDIV to altitude PDIV — the relationship depends on the specific pd product at the worst-case gap in the assembly, and that relationship varies with geometry. An assembly with a 1 mm interface gap behaves differently on the Paschen curve than one with a 0.1 mm gap at the same operating voltage.
Second, sea-level testing does not exercise all failure modes. A void that is too small to produce detectable corona at sea level — because the local field intensity falls below the 3 kV/mm breakdown threshold of air at 101.3 kPa — may become an active corona site at altitude when the effective breakdown threshold drops to a fraction of that value. Sea-level testing cannot detect incipient altitude-sensitive voids. Only altitude testing, performed with corona detection instrumentation, reveals these sites.
This is the reason NASA-HDBK-4007A — the authoritative technical handbook on Paschen and corona design for reduced-pressure high-voltage systems — recommends that designs intended for reduced-pressure environments be analyzed using the Paschen curve for the specific gap geometries present, and qualified by test at the pressures corresponding to the Paschen minimum for those geometries, not only at the minimum operating pressure.
These questions help distinguish suppliers who have thought through altitude performance from those who are applying sea-level high-voltage practice to an altitude application. A supplier without altitude engineering experience may not be able to answer questions 2 through 5 from their own design or test data.
References are provided to support the technical claims in this application note and to allow engineers to verify source material independently. Where standards are cited, the edition current at time of publication applies. Contact our engineering team with questions about how any reference applies to a specific application.