Well I just HAD to bring this up ;D The Volvo 343 had a very short rally-cross career in 1980 but achieved fantastic results for what it ran.
"1980 and the 343 takes off the European Rally Cross Championship. That lusty infant, the 300 series Volvo hatchback, has knocked off the Swedish Championship. There was a new generation of Volvo race-boys at the wheel of two turbo-charged 340's, names of Per Engseth and Per-inge(Pi) Walfridsson."
Stolen from V3M:
"1980 and the 343 takes off the European Rally Cross Championship. That lusty infant, the 300 series Volvo hatchback, has knocked off the Swedish Championship. There was a new generation of Volvo race-boys at the wheel of two turbo-charged 340's, names of Per Engseth and Per-inge(Pi) Walfridsson."
Stolen from V3M:
Early 343 rally cross cars ran the B14 turbos bored to 1.7 with Alpine 16V HEMI-top. Volvo won the European rally cross standard class championship with those early models in 1980, third place was also 343 Turbo and in top10 there were several other 343 turbos in that year too so it was quite competitive car.
EC RC 1980 Final results
Standard
1. PI Walfridsson-S-Volvo 343 Turbo 142pts
2. Martin Schanche-N- Ford Escort RS1800 138pts
3. Per Engseth-N-Volvo 343 Turbo 117pts
4. Anders Hultqvist-S-Volvo 343 Turbo 100pts
5. Börje Carlsson-S-Volvo 343 Turbo 86pts
6. Piet Dam-NL-BMW 320 50pts
7. John Welch-GB-Ford Escort RS1800 38pts
8. Folke Andersson-S-Ford Escort RS1800 28pts
9. Rolf Nilsson-S-Ford Escort RS1800 26pts
10. Hubart Katzian-A-VW Golf GTI 20pts
11. Kjetil Bolneset-N-Ford Escort RS1800 20pts
12. Herbert Grünsteidl-A-VW Golf GTI 17pts
13. Bertil Molander-S-Ford Escort RS1800 15pts
14. Lars-Erik Walfridsson-S-Volvo 343 Turbo 12pts
15. Trevor Hopkins-GB-Ford Fiesta 12pts
16. Mikael Nordström-S-VW T1 Turbo 11pts
17. Gunnar Kittelsen-N-Ford Escort RS1800 10pts
18. Tony Drummond-GB-Ford Escort RS1800 8pts
19. Herbert Breiteneder-A-VW T1 6pts
20. Tore Finnbrathen-N-Ford Escort RS1800 5pts
21. Ed van Schie-NL-Ford Escort RS1800 4pts
22. Walter Mayer-A-VW T1 3pts
Pierre Brunetti-F-Talbot Rallye 3 3pts
24. Carl-Johan Lindblad-FIN-VW T1 Turbo 2pts
Göran Johansson-S-Saab 99 Turbo 2pts
Graham Hethaway-GB-Ford Escort RS1800 2pts
Stig Emilsson-S-VW T1 Turbo 2pts
28. Georg Wassgot-A-Alfa Romeo Alfetta GTV 1pt
Anders Nordstedt-S-Saab 99 Turbo 1pt
Ake "Bryggarn" Andersson-VW T1 Turbo 1pt
Jacques Aita-F-VW T1
Francois Monten-B-VW T1
EC RC 1980 Final results
Standard
1. PI Walfridsson-S-Volvo 343 Turbo 142pts
2. Martin Schanche-N- Ford Escort RS1800 138pts
3. Per Engseth-N-Volvo 343 Turbo 117pts
4. Anders Hultqvist-S-Volvo 343 Turbo 100pts
5. Börje Carlsson-S-Volvo 343 Turbo 86pts
6. Piet Dam-NL-BMW 320 50pts
7. John Welch-GB-Ford Escort RS1800 38pts
8. Folke Andersson-S-Ford Escort RS1800 28pts
9. Rolf Nilsson-S-Ford Escort RS1800 26pts
10. Hubart Katzian-A-VW Golf GTI 20pts
11. Kjetil Bolneset-N-Ford Escort RS1800 20pts
12. Herbert Grünsteidl-A-VW Golf GTI 17pts
13. Bertil Molander-S-Ford Escort RS1800 15pts
14. Lars-Erik Walfridsson-S-Volvo 343 Turbo 12pts
15. Trevor Hopkins-GB-Ford Fiesta 12pts
16. Mikael Nordström-S-VW T1 Turbo 11pts
17. Gunnar Kittelsen-N-Ford Escort RS1800 10pts
18. Tony Drummond-GB-Ford Escort RS1800 8pts
19. Herbert Breiteneder-A-VW T1 6pts
20. Tore Finnbrathen-N-Ford Escort RS1800 5pts
21. Ed van Schie-NL-Ford Escort RS1800 4pts
22. Walter Mayer-A-VW T1 3pts
Pierre Brunetti-F-Talbot Rallye 3 3pts
24. Carl-Johan Lindblad-FIN-VW T1 Turbo 2pts
Göran Johansson-S-Saab 99 Turbo 2pts
Graham Hethaway-GB-Ford Escort RS1800 2pts
Stig Emilsson-S-VW T1 Turbo 2pts
28. Georg Wassgot-A-Alfa Romeo Alfetta GTV 1pt
Anders Nordstedt-S-Saab 99 Turbo 1pt
Ake "Bryggarn" Andersson-VW T1 Turbo 1pt
Jacques Aita-F-VW T1
Francois Monten-B-VW T1
I think the Volvo 16V wasn't around long enough to be made competitive enough before they stopped competing in the rally cross. There were problems with the durability of the head/heat issues with turbo tests, many private race teams from that time reported same. Also the cost in rallying became too high. At one point Volvo even considered participating in Group-B, that's why the 363 prototypes were made. The plan was to homologate the V6 in 300-series so they could race 300-series in Group-B with V6 engines, but during the time racing costs in Group-B were rising sky high when the evolution supercars came and Volvo abandoned the plan.