Are there any design or ergonomic regulations with regard to the pilot's vertical and horizontal vision angles from the cockpit?
For example, pilot should see space 30 deg. above and 20 deg. below horizontal.
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The certification specification for aircraft are deliberately a bit vague on the topic. This allows manufacturers to come up with creative solutions that may have been prohibited if specific angles where required in the specification.
For large aircraft, EASA has requirements CS25.773 in the Certification Specification 25 (CS25) PDF which is included below this answer. The FAA requirements are similar in FAR 25.773.
To make sure that there is an agreed standard on what is acceptable to the certifying authorities, acceptable means of compliance have been published. Manufacturers may deviate from the AMC's if they have good arguments for it.
An example of the FAA AMC on this topic can be found in AC25.733-1 (PDF). The FAA document refers to standard ARP 4101/2 which is the successor of SAE 580B (unfortunately you have to pay for these documents).
From this answer and the image there contained, you can see how the outside visual field of view of the cockpit of the A320 family compares to the 580B standard.
CS 25.773 Pilot compartment view (See AMC 25.773) a) Non-precipitation conditions. For nonprecipitation conditions, the following apply:
(1) Each pilot compartment must be arranged to give the pilots a sufficiently extensive, clear, and undistorted view, to enable them to safely perform any manoeuvres within the operating limitations of the aeroplane, including taxiing, take-off, approach and landing.
(2) Each pilot compartment must be free of glare and reflection that could interfere with the normal duties of the minimum flight crew (established under CS 25.1523). This must be shown in day and night flight tests under non-precipitation conditions.
(b) Precipitation conditions. For precipitation conditions, the following apply:
(1) The aeroplane must have a means to maintain a clear portion of the windshield during precipitation conditions, sufficient for both pilots to have a sufficiently extensive view along the flight path in normal flight attitudes of the aeroplane. This means must be designed to function, without continuous attention on the part of the crew, in –
(i) Heavy rain at speeds up to 1·5 VSR1, with lift and drag devices retracted; and
(ii) The icing conditions specified in Appendix C and the following icing conditions specified in Appendix O, if certification for flight in icing conditions is sought (See AMC 25.773(b)(1)(ii)): (A) For aeroplanes certificated in accordance with CS 25.1420(a)(1), the icing conditions that the aeroplane is certified to safely exit following detection.
(B) For aeroplanes certificated in accordance with CS 25.1420(a)(2), the icing conditions that the aeroplane is certified to safely operate in and the icing conditions that the aeroplane is certified to safely exit following detection.
(C) For aeroplanes certificated in accordance with CS 25.1420(a)(3), all icing conditions.
(2) No single failure of the systems used to provide the view required by subparagraph (b)(1) of this paragraph must cause the loss of that view by both pilots in the specified precipitation conditions.
(3) The first pilot must have a window that:
(i) is openable under the conditions prescribed in subparagraph (b)(1) of this paragraph when the cabin is not pressurised;
(ii) provides the view specified in (b)(1); and
(iii) gives sufficient protection from the elements against impairment of the pilot's vision.
(4) The openable window specified in sub-paragraph (b)(3) of this paragraph need not be provided if it is shown that an area of the transparent surface will remain clear sufficient for at least one pilot to land the aeroplane safely in the event of - (i) Any system failure or combination of failures, which is not, Extremely Improbable in accordance with CS 25.1309, under the precipitation conditions specified in sub-paragraph (b)(1) of this paragraph. (ii) An encounter with severe hail, birds, or insects (See AMC 25.773(b)(4)).
(c) Internal windshield and window fogging. The aeroplane must have a means to prevent fogging to the internal portions of the windshield and window panels over an area which would provide the visibility specified in sub-paragraph (a) of this paragraph under all internal and external ambient conditions, including precipitation conditions, in which the aeroplane is intended to be operated (See AMC 25.773(c)).
(d) Fixed markers or other guides must be installed at each pilot station to enable the pilots to position themselves in their seats for an optimum combination of outside visibility and instrument scan. If lighted markers or guides are used they must comply with the requirements specified in CS 25.1381.
Many aircraft have eye position gauges in the cockpit that pilots can use to adjust their seat for optimal view. They either try to line up little colored balls or look through a small sight. Here are a few examples:
Yes, specific norms related to the cockpit is made by references of angles of elevation and depression so that no pilot feels that they are only running with dependency on various instruments rather than their own eyes. By considerations of the designers and testing pilots, The angles of vision of pilot from the cockpit are suitably chosen by calculations and testing . Also, most of the planes of same class have same angles like airbus a380 and Boeing 747 or an-32 and c130j super Hercules etc.
As mentioned in this answer: yes there are regulations for the vertical view from the cockpit. A complete horizontal and vertical view regulation has been proposed, but has been watered down to an Advisory Circular after protests from the industry.